Which one of the following is an e+ 2n5a wee7y*5szrn.,mxn2grgo v8dzxample of a vector quantity?

  Which of the following operations will not change aek*z zk+ 2oaxj22z5d z vector?

  Which of the following is an8dvq/ w5qo hl.3u1hp8 7okdbl accurate statement?

  The resultant of two vectors is the smallest when the angle betweenzbey9ok46 na a :/jh+s them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, r2co6.(;h0hs ol nhenb espectively. When these two vectors are added, the magnitude of thbc s h0nl;(ohh6n2oe.e sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the f8t6nn-+j * hqlvsdsn4ollowing is a possible answer folnn 8 s*6tv h-4dsjq+nr the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directvoq -b9g2onwd 4ls, n(ions tha( 92nd l,ownsovq -g4bt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unk)4zrn0gprd6 f ;dc -dunown vector is

  Ignoring air resistance, the horizontal component of a projectile'93 ( inrn5re m ge )v6:elxyc5.p9xoiys velocity

  A ball is thrown with a velocity of 20 m/s at fp05v85zmnegqly n+j r. w 6m,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, th9irzid29 1j; t,w+sbep e8s vhe horizontal component of a projectile's accelerationwvj9 rzs9ebe+2id, 1;hs8ti p

  A soccer ball is kicked with a velolyg me0xq:.j;city of 25 m/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 object is directedtmpaak9/4 2vv szzn(2 anti-parallel to the velocity vector,vakstn2m2v/z pz49( a

  If the acceleration of an object is always directed perpendicula:ei mp; 86.ph cqg) m9lod/uozr to its velocity ec/lmpod.;u6hm :)zpg io9q8,

  At what angle shouldpktp.fs83 g q- a water-gun be aimed in order for the water to land with the greatest horizontal ras-k83 .pfpgtq nge?

  An Olympic athlete throws a javelin at four diffe4w;t uupw-0eyrent angles above the horizontal, each with the same speu eywwu-t;p 40ed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 yoepw d 8+*yh-crur hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would drpw+*ch- 8ey be

  A ball is thrown at an original speed of 8.0 m/s at an anli52 tg1gln)w gle 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, how does in*owswc ah0 o2pj 1(hx8ca:i 5ts speed compare to its initial speed?:*08xnjo1oawi 5 hc hwp(2c sa

  A stone is thrown horizontally from the top of a toweg4*6qjzprv: dgg/h sc0p;,f jr at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the l;4*6pgpc j,g0v rjsg z:d/ qfhevel ground below?

  A bullet is fired horizontally, and athph; z 9 qk mt0hgr1t436ih-at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall opa hht0 gq;hth439-1trikz m6f the two bullets.

  A plane flying horizontally at a speed of (yj /8buccx6iirxm*3am;a (d 118.3 m/s and at an elevation of 216 m drops a package. 2.7 secondsj;x6cmimd cb(*y/i x3a8r ( au later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, a4mb qk413k;mdvxuqq 1nd one second later a second package is dropped. Neglecting air resistance, the distance between the falli43 v1q qqxkbm4 1d;kumng packages will

  A pilot drops a bomb from h b3 m7( rqok7yv4jqnxl b76m 0obtklk4+w57 ha plane flying horizontally at a constant speed. Neglecting air resistance, when th4rj 5nb( k7vmhqoxm kyl7t 7lbb4kwqo76+3h0e bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the c vyy 6a*79.es5aput 4ckeyo(Moon is only one-sixth of that on Earth. If you hit a basv6e.c *o9 as(ceypat u y4y5k7eball 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.;2(9i to )arg cw9iq 5d/nfj0rh yptl to a straight, level road and pass a car traveling at 45 mi/h. The relative vei5wyf0rat ondigl9rj/t;c9p q). ( h2locity of your car to the other car is

  You are trying to cross a river q/3h ove2d1l cthat flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bankv/l1 h23oq dec directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take4omqruyk 9+ -vl, k(sr6 lzgam2y g8y; you to mo9-l l4+y2,qgu zvymm8o (k rasrykg;6ve 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees b/x1yx 4 yco/h e8lhcq*elow the +x axis. The y component of A ih x1 yeqhc//oxc*y8l4s

  If a ball is thrown wik wcm6v3knkli.3 )wj1th a velocity of 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 eolaihl71fsra ;i. ,vt9a b,t7 nd up 2.0 km north and several kilometers east. How many degrees north of east have you r b. ih797lavt1,tal;aiosf ,walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vest ak7e 1n8qq) j qh8d:t:yni:locity is 8.00 m/s. The angle between the direction of ij1nqi8ae tdqy8h)n:q 7 :s: tkts motion and the x axis must be

  A 400-m tall tower casts a 600-m mqy55c ;esej;2/oxal long shadow over a level ground. At what angle is the Sun elevated above the horizon?o2sx;;e5mc 5 eljq/ ya

  Two vectors A and B have components (0, 1) 25qm3 xn)7iie; 6(amq x2 gj.ttqkpy hand (-1, 3), respectively. What are the components of the sum of these mga3y7x2qqtp.jt kx2 6)i;nemq hi(5two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. dxy 2g nc:az5w,5-0ynid +broWhat is magnitude ofi 0d5yg n-w d+bncy,x:r2o5 za the sum of these two vectors?

  Vector A = (1, 3). Ve7e/*hoz6t1z qm ;ohuv ctor B = (3, 0). Vector C = A + B . What is the magnitude of7 moehz1qu zho/6;tv* C ?

  A car travels 20 km West, thenb8 )e4c( ud4 h*ki soo+cidx;s 20 km South. What is the magnitude of its displacement?uki) ex hcd44ciods(so;*8 b+

  Three vectors, expressed in Cartesian coordinates, abw-b1 -hpsi; k 4ya(yore
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, expre p zp5fh* m2v:f/)feerssed in 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 = (+3.0, -8.0), w) oa(9bh)x qanhat is the magnitude of )x (o)h9aanqbvector C = A - B ?

  A runner runs halfway around h(ibo azc6l p/e ve(4x+g, ce9a circular path of radius 10 m. What is the displacecel ze , c(+(xe ga6pb9v/hio4ment of the jogger?

  Two forces are acting on an object as shown ,-z+jubw x o)10isrj0sc ydu)in Fig. below. What is the magnitude of th-01 jsu+yowzx)i dr0cj)su ,be resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the dire +0,eyzv;4vi am go-nhction of the -v;+aogm hzv0n, ie4y resultant force?

  Vector A is 3.9 cm long and points along the positive x axis. rc;aixxc j5-- Vector B is 9.7 cm long and points atixra-j;c5 cx- $+53^{\circ}$ 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 70 cm long and poe. nm/y8t pzi ai vc bp+4+(zom1f-0ipints at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 48 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 sp* 86btejogu0deed of 17 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 betue*o 680dgbj 3.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, (v4( bkpuje6lwith a velocity of 18 m/s, from a bridge. It falls 11 m to the water below. How far does the re 6 (blpkvu4(jock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 m above ni i 7iq*p)in:the ground, strikes the ground after travpi* niq)n i7i:eling horizontally a distance of 17 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump w s1wzu2*iy dt6ith a speed of 12 m/s at an angle 6dwzys *2u1ti 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 ju.6-y0j qj5m3o h *k zr+gumhiamp with a speed of 10 m/s at an angle hi5 6 .ok *gj0+a qujy3zhrm-mof $37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initi6cwwhz9p (b1 zal velocity of 21.1 m/s at an angle of $40.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 54.3 m/se0 3ct; uigf.v at an angle of $49.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired 57ua3de/cufa at an 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 horizod u-5oofny(s9nok hsw6uf ;9 7jbp+/dntally at 17.5 $m/s$ from the roof of a building 44.9 $m$ 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 vvlo ;*zs3sth +3au1oinitial speed of 37.9 m/s at an an; ssul vo+1hv *o33tazgle of $37.1^{\circ}$ 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 veq:q aho).osfjq3q f- .locity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take you to finis.fhq:a-.3 s)qoo qqfjh would be

  A plane has an air speed of 200 m/s due Nd 3+m/am0q tuxorth, and is in a wind of 50.0 m/s to the West. The plane's speed re/ mtm0udxa 3q+lative to the ground is

  A plane is flying due South (pg5l,j:ooa:dm x1j c6$270^{\circ}$) 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 o rw,+wu2rhn;t+9x 9yy:iagy2dxev 5wf 120 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 projectile with speed 50.+(hlzi9eru+szl (f11s1 hp oxb, c 1si0 m/s in a f1f 1sso+zh+x er(11(9,czbhsili lup orward 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 a river with q1 ip- ilr7 uv(3n79ll p7qmxhgy ;c6ba current of 6.0 m/s6r uhn- 17 7 mq9lp(37ipygi;bllvcqx. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 18 mb9uz2fwxb : /zj z0jjw3xe9/e/s in still water wishes to travel directly across a river 1.0 km wide in whi: j wzb9zuxb3j xz29/0/ef wejch the current flows at 7.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/sw5epedyj 7m3uut(f 1z(bd 3u( in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream shoulwp1u(e yddu3 t7j fz(53e(mubd the driver head the boat?

  A swimmer heading dirf*(r/ delb5b1x nq7ovop : wh4ectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is s4( oe pdqb5lx71bfwo/hvn* r: wept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches y4, ; ryg(hqhtthe opposite bank in 6 min 40 s. She is swept downstrr,gt(;y4 hh qyeam 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.45 m/s, must aim upstreamw+urte - enab :v4l-v1g;1h kj at an angle ofaeu1 bv1w; :4vt- lgjkrh+e-n $22.2^{\circ}$ (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)  $m/s$