Which one of the following is kw,e) .kin-thn r3,bx2 qvy3nan example of a vector quantity?

  Which of the following operations wil; phkcfj79likle l1 p x8)89sbl not change a vector?

  Which of the following isugqgu ayqwrn,3r pg84y (32)b/4nipk an accurate statement?

  The resultant of two vectorsvghsxfe+ ye 06p5 ae-399,w5nc fm(,jogf ezb is the smallest when the angle between them is

  Two displacement vectors hg 4 0rg0cr)eqvei :x(wave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are a( c :)gg0vwe 0xrerqi4dded, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addesp4(4cuf. j //xc9/fo p/hewo fpacy5 d. Which one of the following is a possible answer for the magnitude of the resultant?y.p5xf ff pc9/ /(oocacps/ ej44uhw/

  Three forces, each having a magnitude of 30 N, pull on a,-mc 41 uj+amyjm ev4in object in directions thm 1e-+m ,jyva4c4ui mjat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownq / avs4c)u.m 9fm)dle30wil r, the unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velcw4spc* - ;wdaocity

  A ball is thrown with a velocity of 20 m/s at anhtl e lyjt2/;gtk)va3-4od 0g 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 horizontal componen2ea2wv+a ia+wy p 6wvq8de3w2t of a projectile's acceleration2a8 va w ae3dy+q6vwiew2+2wp

  A soccer ball is kicked with a velocity of 25 m/s atkf12ju8h8 (k 4ephxy 7vy uo:d 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 mj:oiuyd:vasq 363x +p8hm8p object is directed anti-parallel to the velocity vecto8 xjvm 8+su:p3m 3di:pqyah6 or,

  If the acceleration of an object is always directed pe wp7a4k e6 5j*fqkqe pb6hj(y7rpendicular to its velocitk7be5 hkaq*fwj 6 4pe7qyp6(j y,

  At what angle should a water-gun h27r e+h*4xj z+m .2f2wosrrcg4bx t gbe aimed in order for the water to land with the greatest horizontxr.jeg 7c+2ztbfr42 * 2xmsohgr+wh4 al range?

  An Olympic athlete throws a javelin at four differendgo mbe8v ,/2qripq; /t angles above the horizontal, each with the same ,pbq/evi8 q2m; dorg/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 b8bszm,a7 ejf mv 5wn,:all for the second time. If the ball leaves your hand with twice tfwa mj:n,m7z ,vse5 8bhe 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 speed of 8.0rf 5(4)) ihijghnji 4i s8oqe+ 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 attempt reaches its maximum height, b15f 73fa 5f0zn jqzxphow does its speed compa7zfz0fax3qn1 pfjb 55re to its initial speed?

  A stone is thrown horizontally from the kd5wlcl 0f0 s62cg9f0 d/vnxmtop of a tower at the same instant a ball is dropped vertically. Whicwdxgfsv l9l/c60nk 2cm00df 5h object is traveling faster when it hits the level ground below?

  A bullet is fired horizofqhw; a/sjr -,ntally, and at the same instant a second bullet is dropped fr s;rfjwh/q- ,aom the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed oxpnn-x xop keq,465)yf 65.3 m/s and at an elevation of 176 m drops a package. 5.6 seconds later it drops ayxxpe6qn4- ),k opx5n second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one )n)dr6mgkym 8sby4 zm,h:nth q(7.f usecond later a second package is dropped. Neglecting air resistance, the distancdz(hm8n)k4,u7m s)6bg :hrqt y.mn fy e between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speb+qq/ pzfx 5duf-s+ q2ed. Neglecting air resistance, when the bomb hits the ground the horqpqx+zfb 2/5q-sf ud+izontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth ok0 /saik4use 7f that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) /4es as7ik0ukthat you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relativammnb fg+r/7/ w *tu1ne to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of g/w ft b+m1*/7nn mruayour car to the other car is

  You are trying to cross a river that flows dujm3iptr r /73xw2ehc2 e south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west f22i3rx/htj r3w mce7prom your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will ir v3h/el:;vdht take you to move 12 km downstream, in 3hrd;/lev v:ha river flowing at 6.0 km/h?

  Vector A has magnitude 8.p-4td ,tjqk w70 m at an angle of 30 degrees below the +x axis. The y cot kt7p- 4jd,wqmponent of A is

  If a ball is thrown with a velocity of 25 m/s at n 4uk+axi ee5;zhmhuyj, 3.i ,an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direjtsx ci-5naj w))3n: 6tk r;iuction north of east and you end up 2.0 km north and several kil;sn-nxr3k6 t5 u) jcti:w ija)ometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/w-*o3rz-7loukg +xv gs. The x component of its velocity is 8.00 m/s. The angle between th3zxg l*k-7og +urow v-e direction of its motion and the x axis must be

  A 400-m tall tower casts a 6,ji 57y gnaomhh,s6j+00-m long shadow over a level ground. At what angle is the Sun elevated aysimh,n,ho 7j5 6jg+above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.yqw/y 7oz kf)oftl l)9i.+o2k What are the comwyty).i )2oo7f kfolzq k9+l/ponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-bjv+chpk2 au i01:(bt1, 3), respectively. What is magnitude of the sum of these two vectorsb i :2hjb0ktpa+1c(vu?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Whac/bu92yq n)rwrr0 xd6t is the magnitude)ndr9q0 / ywc rb2ru6x of C ?

  A car travels 20 km West, then 20 km South.34phtx +nls3f What is the magnitude of its displaceme3x4+sthpn fl3 nt?

  Three vectors, expressed in Cartesi+wuizkj+ b7x w;*odz8an 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 coordinates, arejx )b rihm kq8y-ty0**
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 magykeh5*2bq qp :nitude of vector C = A*kqbeh2p yq 5: - B ?

  A runner runs halfway arpjcewk2 t+2 gqo /dd.2ound a circular path of radius 10 m. What is the displacement ofe o.+k/dtwjdp 22 2qgc the jogger?

  Two forces are acting on an object as shown in Fig. below. What is thg 4b:d)kb3*d+bwlx3; szx)iz k (pcjne magnitude ozpg )kdw3xl *(j:4 3;is)cbnkdbx +bzf the resultant force?

  Two forces are acting on an object as shown in Fig.if wv:hde w*: 8j3cur. below. What is the direction of the .w e wi3rujd:8* fcvh:resultant force?

  Vector A is 3.4 cm long and points along the positiy8lp8oaf 10e*hel pt2ve x axis. Vector B is 7.0 cm long and points attee0 l yo*1plhp 2a88f $+46^{\circ}$ 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 88 cm long an** :mfnyui1h+0 mppyy d points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 26 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 withso9i9oo3p9 .fgh a1s r an initial speed of 28 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of thh.ig 999srspo o3of1ae cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, whv a8nfr/(y-hb)szd /ith a velocity of 17 m/s, from a bridge. It falls 22 m to the water below. How far does the rock travy f)vnds/ha(h /r8-z bel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the grounmke , fcjfp 8fe sgz.l9(*kl94,vngbbh- o5d5d, strikes the ground after travelin kmlzlbf4,cepbg.f* 5ks 85h(voengfj99 ,- dg horizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jum)wp z8c2 ;qtn9cp8mvwwt 7wi, p with a speed of 12 m/s at an angle ofp2zw;t 8p c ni,7cq w)wwmt8v9 $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpv9ez1 +twzq:y3w8pnp goes into the jump with a speed of 10 m/s at an angle of qe9yn ptpwz+wv 81z3: $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 55.7 m/s at an angle of mpyp7ei .uy blp*y,v,f tg )ygyj0w8 4k9,aw, $10.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial x:q-yte brv60em);ckm-qyp+velocity of 45.9 m/s at an angle of $33.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at aux:qeecm+ 0l95g7h cs/bm4 knn angle 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 at 25.9 n9+gn6+ b;bqx kk.b cb$m/s$ from the roof of a building 69.6 $m$ 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 lev9st5yfs 8vnagy z0 r. )mefmcyu.9 6manz/;i)el with an initial speed of 61.8 m/s at an angle cm 0zg9 /; 9s nv.y56fm8esa)ynyiu)tm fzr a.of $43.5^{\circ}$ 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 1500-m race at a velocity of 4.0 m/e2vb-t9;a0 rt(ugz l bs. If you ran the same race on a day whale(t;u2 gb0 9vz- trben 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).2h5 zsn c k2fp;xbeu 50.0 m/s to the West. The plane's speed 5hp.scu 2e); bz2x fnkrelative to the ground is

  A plane is flying due South mber)6vui ysa 1mu486f96 sks($270^{\circ}$) 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 km/h is he3hc y*qgr(k t/aded $30.0^{\circ}$ 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 movik5tn:,e,: h ixj/i3j,athvnu ng 200 m/s horizontally fires a projectile with speed 50.0 m/s in a for h:k,v5/ia: tn enijh,j tx,u3ward 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, is directed across +6sj qw ocr*ct;lwpl8;a97ny a river with a current of 6.0 m/s. What8;lwrwol9;p+jc 6q 7 nacyt* s is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 20 m/s in still water wishm-ejjk8)y ,vas g8v3r es to travel directly across a river 1.7 km wide in which the current flows at 3.3 m/s. How )j8vgryk , asv-8ej3mlong will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to 4m8x*jbxtcq 6x(7mkm travel directly across a narro(xtmxbj 67 c*x mmkq84w strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly a+sggoryj j3 g;*:rw g,;t0 t9 gcsfj:gcross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept otcg0:* ;g;jtrjg3sr:j g w+sgyfg 9,downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the l (zo q+ 2gd fz3ub ig)8qh4j3r2ypt4yopposite bank in 6 min 40 s. She is swept downstream 2iylz3(jg q +y)q324zudgtof 8r4bp h480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.56 m/s, must aim upstream at anud(govvd -uy txn)/*8 angle ofyoud)xngv(uv/ dt8-* $22.5^{\circ}$ (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)  $m/s$