Which one of the following is an example of a vector quantic4bslboo6id)jh). 9 w2al 4em ty?

  Which of the following operations will not chaj :(ohtthnq(- nge a vector?

  Which of the following is an accu eml:/h fvuw39xsrt20rate statement?

  The resultant of two vectors is the smallest when the ang 36 xh8)azzdxnp8e5b,wcma h*le between them is

  Two displacement vectors have magnitudes of 5.h4*q+)zv ea ht0 m and 7.0 m, respectively. When these two vectors are added, the magnitudeeahvzt*4)+ q h of the sum

  Two vectors, of magnitudes 20 and 50, ayrt51 y::ry +y3d ts) g8msg9ui1c jatre added. Which one of the following is a possible answer for srsdg935c 1+:yyja8gt it): ur y1y mtthe magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objec7hvz j,,ie vi56ow/uvt in directions thvi6hu, o/57iv,zjvew at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is97(9eax gjz5+j5da23iod wfw: e tnq k

  Ignoring air resistas9 98opf ioay2yjj1:14epssy7 .vecb nce, the horizontal component of a projectile's velocity

  A ball is thrown with a vtk*n h0yii6xuzl 1piz/pfa0;gc i-;6elocity of 20 m/s at an angle of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontaq5fy g +m5t ,*nssjj*(,q * :qxvkcvill component of a projectile's accelerationg, t* vs:m*k*nvqjq+jci,f ( 5 yx5qls

  A soccer ball is kicked with a velocity of 25 m/s ap-5quwq,;io o 5 st.wevato.e5uq o88t an angle of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of an object is didt 8y(epxcw ./ z3,yy+:pajwd rected anti-parallel to the velocity vecty/pd w,3x +yap.c:e8 zyd(w jtor,

  If the acceleration of an object is always directed pertz xp92i 3aayh*o(, rszu i18b/ v8vispendicular to its velocity1rtv 8ss9a h2z/i,i a8x(ip y 3*buozv,

  At what angle should a water-gun be aimed in order for t+sw0qws 4m6+lo gn5+c .b lirv8+x ksshe water to land with the greatest06ibq+glc5ok+ ls.m4srs w+ns+ 8vw x horizontal range?

  An Olympic athlete throws a javelin at four different w2 25zje:efde c.lce: angles above the horizontal, each .cw2e52eld:ezcj:fe with the same speed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for f m7*qlri.o-o the second time. If the ball leaves your hand with twicel rmq. -foi*o7 the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed9. u r:4 jvijc,rxd+sn of 8.0 m/s at an angle of $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a field goal attmw)/maf h9lq- hd-ma4empt reaches its maximum height, how does its speed compare to its initdhlqm mama f/--4 9hw)ial speed?

  A stone is thrown horizontally from the top of a tower at thefgw 2: md(9u *d+nmc- brlpp.p same instant a ball is dropped vertically. Which objlfb.:ddm+ pmpw29gr (u*- pcn ect is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bulln or 6s/mbc+.sx,lr i*et is dropped from the same height. Ignore air resistance. Compare the times of fall of the twosmobi6n.lc, srr +*/ x bullets.

  A plane flying horizontally at a spee/ziz1reta*vv veahg/ ;6(l7id of 82.2 m/s and at an elevation of 249 m drops a package. 4.4 seconds later it drops a second package. How far apart will the two packages land on thz1 ah *(vav ig6zelt7; vr/e/ie ground?

  A package of supplies is dropped from a plane, and one seckql s zc/or)c1gpy6*x3mo:/ yond later a second package is dropped. Neglecting air soy*:/mc)6 kcg z1ryqxplo /3resistance, the distance between the falling packages will

  A pilot drops a bombhazy823 j8re cj6)siv from a plane flying horizontally at a constant speed. Neglecting air resistance, wh)a3ys2cj8zrj8i ev6 hen the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth.t zb rk5kju-z :u91y3soyg7i 4 ox2vu) If you hit a baseball on the Moon with the same effort (and at2k5jr yi-y14to u3k x)g 7bz:vuz9osu the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a s lj6n)qzd3vc/ oxy). e1( zitftraight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other cafo(x/ticz d jv .y 6)zn13lqe)r is

  You are trying to cross a ri 6-rpu:g)prmqi xn t 0pxfb7-r(a)x5vver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank g px6r 0 bq-mx5p)nrfa(7)t:-xprui vdirectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h.b pvbey (q,ev .my5vka t;1)ordn t(: in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 qra k:e; .(bbvo). p (n5tted,yvy mv1km/h?

  Vector A has magnitude 8.0 m at an angle of 30 de hcma jp1*qz:bm5 :b3nq *har+,owq+ygrees below the +x axis. The y component ofhj: *q 1amr+ * +boqm:5nh cwbzqay3p, A is

  If a ball is thrown with a velocity of 25 m/s at an angle ofwgqq+:,i3gb n +diw 5b $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direction nors5,1 y nf1q+e esvh/rqth of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have fyreheq, 1n vs/+q5s1 you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of ixsd b84c0 k(lsts velocity is 8.00 m/ klcbs0(sd4 x8s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level /g,bp( uhr /k* )jtzmwground. At what angle is the Sun elevated above thzmjgb/ u* r(tp ,w/)khe horizon?

  Two vectors A and B have components (0, 1) and a8l h9 gdde9b*(-1, 3), respectively. What are the components of the sum of these*98h9dbadlg e two vectors?

  Two vectors A and B have components (0, 1) and (-9:t7 4 i /wuf;kuxgzr6y lpl3o1, 3), respectively. What is magnitude of 9; 6kfwp 4 3:ulrlz7ou/gxtyi the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vec,y*q3d ) 8luk2ui:z oaqi x1artor C = A + B . What is the magnitude a8*q):xuz doi 3ykr i,u1ql2aof C ?

  A car travels 20 km West, then 20 gtz-ovm- gve4s5 ;k1gs 9cty3km South. What is the magnitude of its displacz;1vm 9-cs 43vsg-tyoetkg 5g ement?

  Three vectors, expressed in Cartesi :ha5(jhoj,*b 6uzd38z owm+.eqqqj 9( a rxoman coordinates, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the magnitude of the resultant vector S + T + U ?

  Three vectors, expressed in Cartesian coordin(;-tv xu9tsk4rxg n3+-sq x e2cg8 wlzm;sk:yates, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the angle of the resultant vector S + T + U measured from the positive x axis?

  If vector A = (-3.0, -4.0) and vector B = (+3.0, -8.0), what is the/ otni181o q7bj wf6) 0 xsn4nayksea8 magnitude of vector C = A - n6 t1/n0oy a)a1f8sbnoiq jkex748sw B ?

  A runner runs halfway around a circular path of radius:q*fk9:uk cb6/j lv zt 10 m. What is the displace9kkzt/:fvq lbu6: cj* ment of the jogger?

  Two forces are acting on an object as shown in Fig. below. What v) 9kp tx(tk1rtjvz/2 is the magnitudetv 1pt)k r/x9(zj2v tk of the resultant force?

  Two forces are actingcih,dkk 9 i qwu,i5+(okff j;9 on an object as shown in Fig. below. What is the direction ok59f,+ou qc,9k khiiiw(jd; ff the resultant force?

  Vector A is 6.0 cm long and points along the positive x axis. Vector B is 8.9l)vsh 7xc7x2c; zi5 z+kd skq0 cm long 9q +c2 ;kzchvz id)7s xs57kxland points at $+39^{\circ}$ to the negative x axis.
(a) Determine the x component of Vector A $A_x =$ (数值)  $cm$ and y component of Vector A $A_y =$ (数值)  $cm$
(b) Determine the x component of Vector B $B_x =$ (数值)  $cm$ and y component of Vector B $B_y =$ (数值)  $cm$
(c) Determine the sum of these two vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(d) Determine the sum of these two vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the posive x axis rotated in the counterclock wise direction) $\tan \theta = $  (数值) 
Please only fill in numerical values in the above blanks!

  Vector A is 51 cm long and points jq9wdd+ hg7k 6at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 29 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A: $A_x=$  (数值)  $cm$ and $A_y=$  (数值)  $cm$
(b) Determine the x and y components of Vector B: $B_x=$  (数值)  $cm$ and $B_y=$  (数值)  $cm$
(c) Determine the x and y components of Vector C: $C_x=$  (数值)  $cm$ and $C_y=$  (数值)  $cm$
(d) Determine the sum of these three vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(e) Determine the sum of these three vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the positive x-axis rotated in the counterclock wise direction) $\tan \theta=$  (数值) 
(Please only fill in numerical value in the above blanks!)

  A stone is thrown horizontally with an initial speed of 19 m/s from the edg b4xogtvifg/5ckl -h*lr; +,de of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom tvd,/* rlib g5k+c;xoglt4f -ho be 2.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 12 m/s, fs)i8tn*p62o )c ioep yzze8ei(pi ,j8 rom a bridge. It falls 22 m to )o,psz ty6)i2*on8zec(8 8ejiippi ethe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally fvm -2c1x8gv hdrom a point 29 m above the ground, strikes the ground after traveling horizontally a distance of 14 m. With what spex d gvhm-28c1ved was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an vvrjt9otg6c 0ivj)qx tw5.+a v1d 30iangle o0j0 x53qvvrav.1 +v g cttwdiio)t6j9f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goehjqbrp aw)q x72t p 67n0.x6mws into the jump with a speed of 12 m/s at an angle m6.t a x27whq6r7 pq0jpbn w)xof $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial v4d fa bk*qid,nu.b*w/elocity of 28.9 m/s at an angle of $32.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched wit7l gbcen8 v5:z;kx tzlh )9s.nh an initial velocity of 54.7 m/s at an angle of $26.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angljt4g 4a;l0lbiyk/f7m0; muid e of $30^{\circ}$ below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

  A projectile is shot horizontally atrmr:6mc5(tzvp,8 tps emk+qz1 m j+7z 24.4 $m/s$ from the roof of a building 65.3 $m$ tall.
(a) Determine the time necessary for the projectile to reach the ground below.  (数值)  $s$
(b) Determine the distance from the base of the building that the projectile lands.  (数值)  $m$
(c) Determine the horizontal component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$
(d) Determine the vertical component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$

  A projectile is fired from ground level with an initial speed of 50.7 m/s at ;0 fa-ac+m8jqcg kn9h an a -8c9akgm0qhcfj + n;angle of $47.9^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.  (数值)  $s$
(b) Determine the maximum height reached by the projectile.  (数值)  $m$
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height. horizontal:  (数值)  $m/s$ vertical:  (数值)  $m/s$
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height. horizontal:  (数值)  $m/s^2$ vertical:  (数值)  $m/s^2$

  On a calm day (no wind), you can run a 1yzd rfca/ - 93rvv0 kv /diywzv*3b)m2500-m race at a velocity of 4.0 m/s. If you ran the same race on a da 2 iadyf0r w3k//yzmv)9vcb- z*vdr3v y when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 5y t12sm1ig. vjqug8k-0.0 m/s to the West. The plane's speed relativ1-y u .ggvtqm1j sk28ie to the ground is

  A plane is flying due Skynt8:bvj*f(w7z i p.py*gr8 outh ($270^{\circ}$) at 500 km/h. A wind blows from East to West ($180^{\circ}$) at 45.0 km/h. Find the plane's velocity with respect to the ground.

  An airplane with a speed of 120 2ctzhmntakn56-:w (b:c gzr/ km/h is headed $30.0^{\circ}$ east of north in a wind blowing due west at 30.0 km/h. What is the speed of the plane relative to the ground?

  A fighter plane moving 200 m/s horizontally fires a projectilyka4/ .ll1mbyp e689vnb ir2we with speed 50.0 m/s in a yk/19v min.2yapb lwb8 re4l6forward direction $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in still water is 8.0 m/s,2+ch v3giw1iausdc 5f629kgx is directed across a river with a current ofwig59ucs+d2v afh6ic1g2 3 kx 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 18whbr26k (xkk sj3e)lrw/z;s : m/s in still water wishes to travel directly across a river 0.8 km wide in which the cu3 s6kzr jkw/() lx;wsrb:hk e2rrent flows at 4.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can mf*bl:sks wu+p5. w mq(ove at 10 m/s in still water wishes to travel directly across a narrow strait in whiw:(lq*bmp wk .ssu5f+ ch the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a rit1 a)ros5p,ea sj9/irver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 4805es1r )itpa 9rj osa,/ m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide rea u0 d-p7v- wu+e/hrm ino2lze1ches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed o z2nl-mw u7eo de/i1-vh ur+p0f the current?

  A boat, whose speed in still water :l/k5g :brc5d9m ebfcis 1.65 m/s, must aim upstream at an angle of c:cb m9ed:gf5 lkr/5 b$19.4^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.  (数值)  $m/s$
(b) Determine the resultant speed of the boat with respect to the shore  (数值)  $m/s$