One car travels due east at eo6) eg tz7x0l and a second car travels north at Are their veloci7x e 6z)olteg0ties equal? Explain.

Can you give several examples of an1e o(okk r vj:uh,j,.ba(lm9y object’s motion in which a great distance is travbh,yj(a 9 oevjkrlu., (ko1:meled but the displacement is zero?

Can the displacement vector for a particle moving in two dhv*si v:r i4j3imensions ever be longer than the length of path traveled by the particle over the same time intervvhv* 4rsi ij:3al? Can it ever be less? Discuss.

$\text { If } \overrightarrow{\mathbf{V}}=\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{v}}_{2} \text {, is } V \text { necessarily greater than } V_{1} \text { and/or } V_{2} \text { ? Discuss. }$

  Two vectors have length xqa+ bl 7w.3te$ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequal magnitude add up to give the zero vector? js4 pll9taev*0b/i p1Can three unequal vectors? Under what conditionebp04p vi*l/sla9 j t1s?

Can the magnitude of a vector ever (a) be equal to one of its componkd7qcfx d2 5h.ents, or (b) be less than one of 5 dqk.x2 c7dfhits components?

  Can a particle with constant speed be accelerating? ----待选择----YesNo  What if it has constant velocity? ----待选择----YesNo 

At some amusement parks, to get on a moving “car”./fno,v.id(kcd8 dlu the riders first hop onto a moving walkway and then onto the co .l,dkd8icn fd .v(u/ars themselves. Why is this done?

If you are riding on a tgj9vn;b x:sm (rain that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backward. Why9js nv( ;b:gxm?

If you stand motionless under an umbrella in a rainstorm where the dr:kaler,i h6ac(w/ u+vops fall vertically, you remain relatively dry. However, if you start r :+iaur(kv h6w/ea,clunning, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, movingl)*(rmrn(qnj vk49u2j(hu y x at constant velocity, throws a ball straight up into the airjum2 u)(4 k r(v(yqlr*9xjnnh in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed i;h4w,p,h0 n mngc wn6in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite sidwhp0 6n,n4g; ciw ,mhne first? ----待选择----AB 

How do you think a baseball player “judges” the flight of a fny 8pgzxz19l pzt.g; 0 r0qe8sly ball? Which equation ig 0p tr8 epzg qy9xzs81.lz;0nn this Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How s9je jth *igm0*cgj )k1hould your angle of aim depend on the distance toig90 *k j1)tejgjmc h* the target?

  A projectile is launched at an angle of -7 lcy+i ph+ly$30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired fr9v0p x qx0m3 dr1p,bgbom the ground with identical initial speeds, but with x 3bpxv1q0rg,b0p m9 d$ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km west and themh36kb r1sc7vccna 5e p/e7;vn 85 km southwest. What is the displacement of the car from the point of origin (magns/ 3ec7pm1cb5 evvr7 ;cn h6kaitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south9mxjg 0dv /rh8fq- t+ /pa8mk2* yaqiw. What is its final displacement fr/mafhyq*p8jm+/atrwi 0 2-kvd98x q gom the origin? Assume the blocks are equal length.    blocks

$\text { Show that the vector labeled "incorrect" in Fig. 3-6c is actually the difference of the two vectors. Is it }\\
\overrightarrow{\mathbf{v}}_{2}-\overrightarrow{\mathbf{v}}_{1} \text {, or } \overrightarrow{\mathbf{v}}_{\mathbf{1}}-\overrightarrow{\mathbf{v}}_{\mathbf{2}} ?$

  $\text { If } V_{x}=6.80 \text { units and } V_{y}=-7.40 \text { units, determine the magnitude and direction of } \overrightarrow{\mathbf{V}} \text {. }$ magnitude    units direction    $^{\circ}$

Graphically determine the resultant of the following three vector lnci0 - 0cy6kki6 k(3 yq v:,xsldhq6idisplacements:6l0klchisq yyk,xc3( :6 qi0nd v i6-k (1) $ 34 \mathrm{~m}, 25^{\circ} $ north of east; (2) $48 \mathrm{~m}, 33^{\circ}$ east of north; and (3) $22 \mathrm{~m}, 56^{\circ} $ west of south.

  The components of a vhliw;mc / ni25ector $\overrightarrow{\mathbf{V}}$ can be written $ \left(V_{x}, V_{y}, V_{z}\right)$ . What are the components and length of a vector which is the sum of the two vectors, $ \overrightarrow{\mathbf{V}}_{1} $ and $\overrightarrow{\mathbf{V}}_{2}$ , whose components are (8.0,-3.7,0.0) and (3.9,-8.1,-4.4) ? components (a,b,c) a =    b =    c =   
length   

  $\overrightarrow{\mathbf{V}}$ is a vector 14.3 units in magnitude and points at an angle of $34.8^{\circ} $ above the negative x axis.
(a) Sketch this vector.
(b) Find $V_{x}$ and $V_{y}$ .$V_{x}$ =    $V_{y}$ =   
(c) Use $ V_{x}$ and $ V_{y}$ to obtain (again) the magnitude and direction of $\overrightarrow{\mathbf{V}}$ . magnitude =    direction =    $^{\circ}$ above - the x axis
[Note: Part (c) is a good way to check if you've resolved your vector correctly.]

  Vector $\overrightarrow{\mathbf{V}}_{1}$ is 6.6 units long and points along the negative x axis. Vector $\overrightarrow{\mathbf{V}}_{2} $ is 8.5 units long and points at $+45^{\circ}$ to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum $\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}$ (magnitude and angle)

$ (a) V_{1 x}$=   units $V_{1 y}$=    units $V_{2 x}$=    units $\quad V_{2 y}$=    units


$\left|\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}\right|$=   units $ \quad \theta$=  $^{\circ}$

  An airplane is travelingkk: ti);s9-mm l4cojy $735 \mathrm{~km} / \mathrm{h}$ in a direction $ 41.5^{\circ} $ west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h ?(a ) $ v_{\text {north }} $=   $v_{\text {west }} $=    (b) $\Delta d_{\text {north}} $=    $\Delta d_{\text {west}}$ =   

  Three vectors are shown in Fig. below. Their magnitudes are given in arbitrary 4(ikm8cgxp 3 wunits. Determine the sum of the three vectors. c kw 3px4mig(8Give the resultant in terms of (a) components, (b) magnitude and angle with the x axis.


$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{x}$ =   
$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{y}$ =   
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  $\text { Determine the vector } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}} \text {, given the vectors } \overrightarrow{\mathbf{A}} \text { and } \overrightarrow{\mathbf{C}} \text { in Fig. below}$



$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  (a) Given the vectorsq irw ftbrz8 di v0/mha- /z7+)6gyp7m $ \overrightarrow{\mathbf{A}}$ and $ \overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


$|\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}|$ =   
$\theta_{B-A}$ =    $^{\circ}$above -x axis
$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ }\text { below }+x \text { axis }$

  $\text { For the vectors given in Fig. 3-32, determine (a) } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}} \text {, (b) } \overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}} \text {, and (c) } \overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}} \text {. }$




$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below +x axis
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$
$|\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis

  $\text { For the vectors shown in Fig. below, determine (a) } \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}} \text {, (b) } 2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{C}} \text {. }$



$|\overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis
$|2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}+2 \overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below + x axis

  The summit of a mountainle:gf t0ken),, 2450 m above base camp, is measured on a map to be 4580 m horizontally from the camp in a direction,) ek:g0elft n $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vectp0mua4 1na2np g :svcvf 7kv24i+ .rvnor in the xy plane that has a magnitude of 70.0 units and a y componenm7vk4:ra 0via pnupnn c4g+s2fv2v.1t of What are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with (5/g rms:w ppon 7cnr2a speed of How far from the base of the rock will s:7g( o 5rpws2 r/mcnnphe land?    m

  A diver running dives out horizontally fk)0d3h a 8kf rqgm)cqy+wy.n( rom the edge of a vertical cliff and 3.0 s later reaches the watery nh(wqd y)k8 .0cq)g+r3kamf below. How high was the cliff, and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of At what angle(sp;1zni ) ojl8g) shouldjpg8 ln i1z;)o the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he wants the pebb6gpbq:v0w b*c les to hit the window* :c6g0q pbbvw with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontallq ahena:8 ijq3gt( 6dhe+2rv*y from the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s initih2gtqranhv6(q8*d ae eji+ :3al speed?   

  A football is kicked at ground le pfhqo rhud,97c)/-ybvel with a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from theghx:z5 *tkh(8zvev 0jqt 6s )8t xhi(i roof of a building lands 36.0 m from the base of the building.*ixhes h(6qz 08z(v5h:xkg tti8v tj) How tall is the building?    m

  An athlete executing a long jump leaves d7a+;6thzn zx3og8lg the ground at a 28.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on the5mmu sv2 6c2fc Moon as compared to the Earth if the takeoff speed and angle are the same. Thef5m6c mus2 vc2 acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directlyewi hj u a.4v2+c+kap1 at a target (on the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wants9 ,3/0.mvli h)bli +tfrdci jk to drop supplies to flood victims isolated on a patc0/+lcd).3jtiihlk m r,i9vf bh of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?    s

Show that the speed with which a projectile leaves the ground is equal to its speed just before it strikes the ground at the end of its journey, assuming the firing level equals the landing level.

  A projectile is fired e+ns)8bb e j*38yede2:ey uliwith an initial speed of at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 .mq+;fpjjiz 5 oaj5noa h21gz ;i9 ev8m above ground level with an initial speed+e8ja on;iq.1jf5a zz9mhoi5gj2p v; of at an angle of 37.0º with the horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an ix l)ki x0se+f1 z;at. n,u9ro)deux(xnitial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a proq *fny2f:2zfpjectile equal its maximum height? fq2nf:yp2 *zf   ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshom,rk5va r4mnco o wdql 1+/u-4w6s7vht is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.s6k1 m w 5amhvw dl4r/4-7no rv,qu+co

  A rescue plane wants to drop supplies to isolated mountain climbers on a rocpbr/689mf zijky ridge 235 m below. If the plane is traveling horizontally withmzjfr6 b98pi/ a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

(a) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. a)?    m
(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down)  ----待选择----updown  should the supplies be given so that they arrive precisely at the climbers' position (Fig. b)?    m/s (fill in magnitude here)
(c) With what speed do the supplies land in the latter case?    m/s

  A person going for a mosxkm( nd)/u(q hfc 2*yczi);qrning jog on the deck of a cruise ship is running toward the bow (front) of the shq; )ncfu(cd /ikhmx)zq(sy 2*ip at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a speed of p pyydc0s2)b ,)cv8uk 0.60$ \mathrm{~m} / \mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$ \mathrm{~m} / \mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    $^{\circ}$

  You are driving south on a highway a(ybx.isri ;us s;2,zit 25 $\mathrm{~m} / \mathrm{s} $ (approximately 55$ \mathrm{mi} / \mathrm{h} ) $in a snowstorm. When you last stopped, you noticed that the snow was coming down vertically, but it is passing the windows of the moving car at an angle of $30^{\circ} $ to the horizontal. Estimate the speed of the snowflakes relative to the car    and relative to the ground.   

  A boat can travel 2.30h7(np1 mip i/ 9 kllpiap9w0m; c1u0tk$ \mathrm{~m} / \mathrm{s}$ in still water.
(a) If the boat points its prow directly across a stream whose current is 1.20$ \mathrm{~m} / \mathrm{s}$ , what is the velocity (magnitude and direction) of the boat relative to the shore? magnitude    direction    $^{\circ}$
(b) What will be the position of the boat, relative to its point of origin, after 3.00 s? (See Fig. below)diraction =    awayfrom the starting point,angle =    $^{\circ}$ relative to the shore

  Two planes approach each other head-on. Each has a speed of and theyi. iwwbs- g29vj +a4ov spot each other when they are initially 11.0 km apart. How much time do the pilotsois. w9+gi 4-bvvw2ja have to take evasive action?    s

  An airplane is headin(.xfl.h r0 d,gc*cf3f5 m rqlvg due south at a speed of 600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Problem 41 so thattazp +v2i0+ ip it will fly due souta0t+vi+ p2 ipzh?    $^{\circ} $ east of south

  Determine the speed of the boat withl od9ft7injl+-ck(k ,x6l,t d respect to the shore in Example 3–11.   

  A passenger on a boat movi9gaipmf9vk,3fz gj, 7 ng at 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in stillrf oi7lqcg23hnl1l-5 water is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed i 45e,j.r;rdknvmv8 ycn still water is 1.70 $\mathrm{~m} / \mathrm{s} $, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45$^{\circ}$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swimming d3refu9mrym-m,9n z6)slrp-yw* -n z 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swimming 7 :e4k,3pzb4czlazgb 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed is 6d(d9dtj(q p2d1 3p0w mv zaff620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police car, trav;p+795nn *vvpv/uxltalmz8 i eling a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

Precisely 1.00 s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is 2.00 $\mathrm{~m} / \mathrm{s}^{2}$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?   

  Assume in Problem 50 that the speeder’s speed is not known. If the police caq5vs w*zwae w5lwo1*0,y ki0 dr accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was loy q500a*s ie,w wwdw51zk v*the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (Fig. below)6 4bxm.jx bbc:. Car 1 travels at abb6.c xb 4xj:m speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple ato+o:+ky))foprcyk z (yp his son's head from a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speey(p )rk:+zco)kofyy +d of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, wb r6 ca)h7hw)ralks 50 m east and 25 m south, and then takes an elevator 10 m down into the base7)ah wb6hrc) rment of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

The result is that the displacement is    m , at an angle of    $^{\circ}$ South of East, and    $^{\circ}$ Below the Horizontal.

  On mountainous downhill roads, escape routes are sometimes placed to the q mn0 ;2avnmz,side of the road for trucks whose brakes might fail. Assuming a constant upw, aqvz;2 mmnn0ard slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

$\text { The horizontal acceleration is } a_{\text {hoiz }}$ =    $\mathrm{m} / \mathrm{s}^{2}$
$\text { The vertical acceleration is } a_{\text {vert }}$ =    $\mathrm{m} / \mathrm{s}^{2}$

  What is the y component of a vector (in the x y plane) whose maqg3eo /vstht z. /;ldg4js6)hgnitude is 88.5 and whose x component o) .qg/zhss4 3gl6t t/vd;hjeis
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an ang i mzwrjc-29 j-undz*2le $\theta=30^{\circ}$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20 \; m/s$ (a) what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?    $m/s$
(b) what is the speed of the raindrops relative to the train?    $m/s$

  A light plane is headed due south wik4*/ f un /0wn1fva-skft ms)oth a speed of 155$ \mathrm{~km} / \mathrm{h}$ relative to still air. After 1.00 hour, the pilot notices that they have covered only 125 km and their direction is not south but southeast $\left(45.0^{\circ}\right) $. What is the wind velocity? $v_{wind}$ =    km/h $\text { The direction of the wind is } \theta$=    $^{\circ} $ north of east

A car moving at 95 2x5w s-ae/ddcpv h2m.$\mathrm{~km} / \mathrm{h}$ passes a 1.00$-\mathrm{km} $-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75$ \mathrm{~km} / \mathrm{h} $, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

  An Olympic long jumper *q66, ybfqfreis capable of jumping 8.0 m . Assuming his horizontal speed is 9.1 q*,frbqf6e 6y$\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “ni-n qvs(8b-rsxmz70d/-w e bs fne iron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleratiode bw0/( fsm-8qzv- bsn7rs-x n due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the 7)1 ,dqi )y2qbsd:xtjy.hd9 uf.5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of +4 ja6cboo9 mnr,gs1kAcapulco push off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend oujkonm9a 1sr+,b6o 4gc t into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minimq35 11qel bvfjum speed is required for the ball to clear the 0.90-m-high net abqb15lf13e q jvout 15.0 m from the server if the ball is “launched” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a co/4cqc.i b njs.nstant $215 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155$ \mathrm{~km} / \mathrm{h}$ on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released (Fig. below) ?



$\theta=\approx $   $^{\circ}$

The speed of a boat in still water is v . The boat is to msw,v. -y i.tjlj. jbu-ake a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance ,.vi- j. jt-yulb.sw jD if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from ground level to,o0j nyxg 0olo3 73zxk the top of a cliff which is 195 m away and 155 m high (see 033onx 0k,x yoozljg7
Fig. 3-47). If the projectile lands on top of the cliff 7.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.



$v_{0}$=    $ \mathrm{~m} / \mathrm{s}$
$\theta$=    $^{\circ}$

  

(a) A skier is accelerating down a 30.0$^{\circ}$ hill at 1.80$ \mathrm{~m} / \mathrm{s}^{2} $ (Fig. 3-48). What is the vertical component of her acceleration?    $m/s^2$
(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 335 m ?    $s$

  A basketball leaves a player's hands a)n- 9liv8 0tkt ul4slit a height of 2.10 m above the floor. The basket is 2.60 m above the 9 ts0vl8ui i-tn4ll) kfloor. The player likes to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the end ofwdi f7ls7uxe; wp25 h- a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make hiswxw y*x,imm.div6 ,m 4 car jump over eight cars parked side by side be ii6v4mx,.m,wyw*dxm low a horizontal ramp

(a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars, and the horizontal distance he must clear is 20 m .    $m/s$
(b) If the ramp is now tilted upward, so that "takeoff angle" is $10^{\circ}$ above the horizontal, what is the new minimum speed?    $m/s$

  A batter hits a fly ball which leaves the bat 0.90 m above the groundunzenz:1 kp9epbtlp:bs . 7+; at an angle oft+z 9p.k1s; 7bppb:l nu:e ezn $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a basebymk11* .u datyall with an initial speed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of a building with an initial veloh l(l e1em13trz:;mx gcity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart yd+3 yat:::ikpasr )v-ver)yzlz42a gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizo: a-p ::ye syi)2ztzay3dv+ l) arvrk4ntal range of your gun?