Which one of the foll-e94te3uy1f5nxc bkv :9k j piowing is an example of a vector quantity?

  Which of the following operations will not change a vectoo2on8 y8 ly796 lpkksg,dqv1 rr?

  Which of the following is an accura.q he mc8ur5 qw)sy-egp4.pa8te statement?

  The resultant of two vectors is the smallest when the angle bq(g* goc dj6yj5rrl5; etween them is

  Two displacement vectors z* hj+ly75onf have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the mof l5nz j*y7+hagnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whicix4 :ja;/)a) h wgfexgh one of the following is a possible answer for the magnitude of the resul)aiaxg:fj w;)xe hg/ 4tant?

  Three forces, each having a magnitude of 3c -jn1:-gckuq;cu -h/ oo ne.z0 N, pull on an object in directions that ar jzguok-n.e1;-:c- cqocu h /ne $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the176t uyu,buvr unknown vector is

  Ignoring air resistance,l hv5bl0p,vvzxocl7 hy0q1( , the horizontal component of a projectile's velocity

  A ball is thrown witgir9 s+qnb(b86yxk*v at7iy3h a velocity 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, tl:, 6w*j4d flu.b4:z(r hupipq6qnno he horizontal component of a projectile's acceleration 6rpizuuq( wb: nfd*h:4olq4j,6. nlp

  A soccer ball is kicked with a velocity of 25 m/iyrb 0(g/ njh*s at 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 objl(4bpgll 05glect is directed anti-parallel to the velocity vec 0g5l4lgl l(bptor,

  If the acceleration of an objecfv jxh8u,ud3 :t is always directed perpendicular to its velocity,u3j8 :d,hf uxv

  At what angle should a water-gun be aimed in ordea bf 9mf9w8capx/p-,jzkds9;r for the water to land with the greatest homw zpja8-/x 9 cbpdaf9;k,fs 9rizontal range?

  An Olympic athlete throws a javelin at four different angles above the h0 frv lnuf,oxrz8b jo c)wv w9x.p-:l-lam,+6 orizontal, each with the,v0 owa6ou z9,+.lc: flfr)wp rj xvb-l-mxn8 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 the second time. If the ball leaves your hanb x/ jf3n5p2ju,n0r ukubf,4sd with twice the velocity it had on your first throw, its horizontal range R (comparsju,jnkb /f5puf u 3 0nr4bx,2ed to your first serve) would be

  A ball is thrown at an original speed of 8.0vn oi 5ri5u8l. 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 fi i3ktm8fo i- liy ma1839 1yihwxu34aheld goal attempt reaches its maximum height, how does its speed compare to its initial speed?1okx3 w ha- if1i4ia ymit3u8m8l3hy9

  A stone is thrown horizontally from the top of a tower at thef5fi/ dhly **y same instant a ball is dropped vertically. Which object ihyf*fi/l * yd5s traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is wq n .t):( yanlh 7(1n23mylsg+zhwdbtnw,8q dropped from the same height. I)g81qt.: q2,nhy 3y+ l(nlhbn7 znwaw dts(wmgnore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 64.7 m/s and22 y6krk v4j-p0zgtvf at an elevation of 269 m drops av v- k6zjr2fkpt4g y20 package. 7.0 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is d-x c(ukwwri7vh.81cinn9op5 ropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between tp(5 uvwi7n nr-c89.oic 1hx wkhe falling packages will

  A pilot drops a bomb from a plane flyi66i-u9lkz58 j v crphbng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of t -zpur6l98 kj hcv56bihe plane will

  The acceleration of gravity on the Moon is only one-sixth of that49c:dup0f bnn wv)2tit2 jwb; on Earth. If ycjn0u:bfib p vw;94dwn t22t)ou hit a baseball on the Moon with the same effort (and at 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 straig bi0k qls2*zw7ht, level road and pass a car traveling at 45 mi/h. The relative velocity of your*sqizlk2 0b7w car to the other car is

  You are trying to cross a river that flows due south with a strong current. jgq88kspaifc0 6 :-3s ek8 ixlYou start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your6kxk8lp :c8aqi3f j sisg-e08 motorboat

  Your motorboat can move at 30 km/s 5 o2r ilqll/.;okxu.h in still water. How much time will it take you to move 12 km downstream, in a river flowing at .lir xso2ulq/5.kl ;o6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the fwc5:g f38o9asnui(m+x axis. The y commc5gf:o(awi9s fn8u 3ponent of A is

  If a ball is thrown with a velocity oe z, veuj ;iu*6l7 c5dxypfy6*f 25 m/s at 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 direction north of east and you ey0rn /b -mgg)dnd up 2.0 km north and sev gmrdny)-bg/0eral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 mf01d lz*g(k x(8 xxgsx9ua0yj/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its m0 xfdu yjls8xx*a9 xk(01 z(ggotion and the x axis must be

  A 400-m tall tower casts a2kv/xp:( r9mi4s bvzx 600-m long shadow over a level ground. At what angle is the Spis :9( x4z vbkvr2/xmun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-6.kr t4uwas i01, 3), respectively. What are the components of the sum otau 06isk 4.wrf these two vectors?

  Two vectors A and B have components (0, 1) and (-1 jah1fy r0f2:i, 3), respectively. What is magnita f01ih:fy rj2ude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C bs kxy,/ s4.ef= A + B . What is the magnitudesebfk/,4sy . x of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude obrv8dt l7m0/s.k -vb xf its displac 0br lvsb-t8/m.v7x kdement?

  Three vectors, expres b9gor91ml)fssed in Cartesian 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 in41 1 e28 y-gbydn/i vinicsfb: Cartesian coordinates, 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 =y/raq.ske9 9c9la y;w (+3.0, -8.0), what is the magnitude of vector C = A - ec.lak rw9;ay9y9 s /qB ?

  A runner runs halfway ar a.yf2 q-voffe:qw8.round a circular path of radius 10 m. What is the displacement of the joggy2a q.fwqoevr :f-8 .fer?

  Two forces are acting on an 2r,yhczp (gq;object as shown in Fig. below. What is the magnitude of the resultant forc2ypr, ;(zgq hce?

  Two forces are acting on an object as shyuj 8rcj03h75b zwg0y own in Fig. below. What is the direction of the resultant forgybyj 08cwz7 u 05jr3hce?

  Vector A is 4.4 cm lor5d4dtjd .k zdzg p:6)*nno c+ng and points along the positive x axis. Vector B is 8.5 cm long and p54 onrd)6 +zznd:cjd*.kpgt doints at $+22^{\circ}$ 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 76 cm long and poic00l x hnb2lkl4uge689 toe;pnts at $30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 31 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 i r/v)zejj22 exbce 5e1nitial speed of 26 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.ee5xjbev rj/ 1e)c22z 7 s. What is the height of the cliff?

  A girl throws a rock hoc, ( 9min5uap3l8mf garizontally, with a velocity of 15 m/s, from a bridge. It falls 12 m to the water below. mc l (ap3g5a,imf89 nu How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, strikesoraz2sm 5f-eh 78k*24wne6y janqz *u the ground after travelkeqz4 jn fw6s2zr*a5h *enmoa2 yu7-8ing horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the j 7 /;chtjo0 ozfp3kl3zump with a speed of 12 m/s at an angle ojko/cf0 ;lt3 zz37ph of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into the i5pziau.glt* y6odli)99o l 74tlexbev/p3 ) jump with a speed of 14 m/s at an angle op9oui)ze5.e3pt*vaiot6l97yx dl/4 blil)g f $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an 0qd- 35v6htp f fp :u7aecmkj0initial velocity of 27.2 m/s at an angle of $44.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 34.3 m/s at an anglf/6wsks 0jd4-s 4( b4tnqjiwye of $23.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle o6,ia/ pnvp7 m x+vk:4mb7t tcwf $30^{\circ}$ 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 hor5z6 c0 e,jsjkuizontally at 27.8 $m/s$ from the roof of a building 31.1 $m$ 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 s7e0ma ppaf 0 nlg-x.f5peed of 38.2 m/s at an ax-a an7gf0.5 mpp0el fngle of $37.9^{\circ}$ 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), vd;qo(bm2v z /a)*jomyou can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind;dbvj*oq v/ (za2 mmo) 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;54dv sbz wj7b wind of 50.0 m/s to the West. The plane's7sbjz5 v d;b4w speed relative to the ground is

  A plane is flying due Souha2x9yfqv .2wz+m * zdth ($270^{\circ}$) 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 km5,ds/ 9zls ops/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 projectile with s l08o kg6me, kvzu)fb2peed 50.0 m/s in0,ekf)l 2 zumv6 gb8ok a forward 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/) a 17qkrwco l4.xvcu.0 m/s, is directed across a river with a curr1l kovc7uaw/cq r)x4. ent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can) z -h+o8c:wqe8ypx hm move at 13 m/s in still water wishes to travel directly across a river 1.0 km wide incw)mexhqh op-y+8:z 8 which the current flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishe t n(skw d6du-x9a*ij1s to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driv w-169xdta(dk ni*jsuer head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bn /cs4 3d,mlq.+ ygkugank in 6 min 40 s.c.3s+nkg u4d q/ l,ymg She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 :m3 a /ut;zeh+rbqlhw9d.)n lm wide reaches the opposite bank in 6 mn: ll9 h);meqrbz t3+d.auh /win 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.16 m/s, must aim upstream at an qm.3zs4p8f4xj .t kddq,y/mv angle ofyf,dx. ./8p vmdjz3t4 m4k sqq $30.9^{\circ}$ (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)  $m/s$