Which one of the followinmvrd/ r* *d/yqg is an example of a vector quantity?

  Which of the following operations will n-d,o8cuat ..ix4l nbq.afc+oot change a vector?

  Which of the followin:tvp(hk/i :icu1e i w.g is an accurate statement?

  The resultant of two vectors is the smallest when the angle between the 2ry9)qs.zj d:a grm5im is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivv z40vw3nu4h bely. When these two vezvnh wb04v43 uctors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addedpxh t5+cfs.5i . Which one of the following is a possible answer for the magnitude of the resultant? hxfic+p5ts.5

  Three forces, each having a magnitude of 30 N, pull on an object*71b oxi)do ()jbvp: vga ;vdfq5qu.l in directions that a:)dfbv vq .boi;1 7ljdpv*xu)a go(q5re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, 0 zr7paxx 3ns*i6i0hythe unknown vector is

  Ignoring air resistance, the horizontal componenl fa49f bjf1u/6r5tfo t of a projectile's velocity

  A ball is thrown with a velocity of 20 m/h qt0q:2+v :a xpnyjh3s 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 horizontal component of a proj 4ywgwq9y(d-8:f: s7pot gcgdectile's acceleration fogty p7w-wq d8gg49:s (dyc:

  A soccer ball is kicked wyg3(/ t rcsfde.wg u//sr99onith a velocity 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 directed anti-parallel to the ve6. w57pquj*iu+cv .(u alxar llocity 6w7q ru(l. p lau*ju vx.ia5+cvector,

  If the acceleration of an object is always directed perpendicular to its (a7,so1qn yu tvelocit(onsqy 7ut1a, y,

  At what angle should a water-gun be aimed in0 -2cmyypjor 6lc q56c order for the water to land with the gre6pq2clc5c jyr - y0mo6atest horizontal range?

  An Olympic athlete throws a javelin at four different angles aborm*kz3.y plzepom9 t + 3(y+py0 vyh+yve the horizontal, each w o3yp* .z9rz y+3kty 0(m +hpp+eymylvith 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 balcv v7si5 .nhp6l for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, itvins76.pvc5 hs horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at anuu6u ;iib;e( r 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, ho-udkqm8yuq v bkc5/; dl6r7c1w does its speed kq ulcq6;y8r/dd1vm cbuk5-7 compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the vwl)6k 25t saw)2xdvv same instant a ball is dropped vertically. Which object is traveling faster when it hits the5vt dsv)) kwa2xw2lv6 level ground below?

  A bullet is fired horizontally, and at the same instah35rmtp-dw:y nt a second bullet is dropped from the same height. Ignore air resistance. Compare thrph:twym 5 d-3e times of fall of the two bullets.

  A plane flying horizontally at a speed of 99.2 m/s and at an elevation of 208 m1u c16f5t;0efqvfu fw drops a package. 4.2 vf50c f1 wqeu6t1u;ff seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped frolh tfgp07-ko/ m a plane, and one second later a second pack-0 tfohp gk/7lage is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant sp54wouz -l9pw *k pua6piy5 fd0eed. Neglecting air resistance, when ou-4ypd zup0p wi56k *9fa lw5the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only o7lju*;x)nz:;w;t u4b2n2rfu ynk dqgne-sixth of that on Earth. If you hit a baseball on the Moon with the q2wk;xg27u :*jtfdun)n ;znl4y r;ub 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 str )1xe t9qmvl:xf+t *tpaight, level road and pass a car traveling at 45 mi/h. The e)1:x 9p*m tx+tvqlftrelative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a u v fh(4 h2xjdnomc944crf10ystrong current. You start out in your motorboat on the east bank desiring to reach the west bank dirorcmx4 1v94cjfn4 hu( yh f2d0ectly west from your starting point. You should head your motorboat

  Your motorboat can move aswdqge s .-d- 42lx4gpqerw4.t 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing apqw r.ws eg42 qxd-g-.44seldt 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 deg2kflx:sl9 pxs43 vfnsx1:6 xyrees below the +x axis. The y component of x3f4 :lx2p x n6svx ysflk9s:1 A is

  If a ball is thrown with a velocity of 25 m/s at)rn5 woq3z* gy an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a stra- u*m+p)8ogy ul9;f xju:wc c+ajd; idight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees no*u)jwc;diuco8g9 +fxlp m ; a y:dj+u-rth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its veloz6l j9kl*q g /p-+8u)x ux.30uoxcrp wwxsg 0pcity is 8.00 m/s. Th pxp jrw/* .-opxu8l) sl0 g3zg60xqkwu9x+ cue 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 ground8vdcl;im1 xa q c+:g6b. At what angle is the Sun elevated above the i1gcbc ax8:q lvm;6d+ horizon?

  Two vectors A and B have components (0, 1) and (-1, mb11hb m/ gl;d3), respectively. What are the components of the sum of these two vectors?dhbm;/1 1bm gl

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What x 1i h-0wtl6b l o6gs(q -d1.hrmxk*xuis magnitude of the sum of thehktlx*q6r0m- g.l 16u( x hxid w1s-bose two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What i w237c0,xov dnwmzn9um .aw3 ks the magnitudenw3x9 .ozwcdnw70va,umm23 k of C ?

  A car travels 20 km West, then 20 km South. Whazr, 4s8 fst(de8kv./k xf1urat is the magnitude of its displacementkr,8zrt/ v1f.k (8sduexa4s f?

  Three vectors, expressed in Cartesia 0./dmvmc6,3cqscd uu+nt x3e7t; tf gn 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,p* i:zp ppk93j 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) an/bdvu- u)qbid4o g;( ).cm lued vector B = (+3.0, -8.0), what is the magnitude of vector C = A i.ebo;u/d)cdv4( m bqu -)lgu - B ?

  A runner runs halfway around a circular path ow1*b / -yvupdqf radius 10 m. What is the displacement of the j1q* -wbyv u/dpogger?

  Two forces are acting onu60zv s3sdw 8e an object as shown in Fig. below. What is the magnitude of the resulta 83sudv sewz60nt force?

  Two forces are acting on an object as shown in Ftd8zh8xh lf nfm5h5x r(;ik-,ig. below. What is the direction of the resulfi;k-5rd5(lx8hx,m zf t 8n hhtant force?

  Vector A is 3.7 cm longl:o +k8r)naug and points along the positive x axis. Vector B is 6.7 cm long and pointn)l ko 8r:u+gas at $+58^{\circ}$ 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 72 cm longf2 7tuzy*7 cfq(a-y :/eqyjx *fwzle1 and points at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 23 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 horizonthi yglrc a 5xs4(-gsmo3z0 p0 b:.2ghf ta:d2dally with an initial speed of 12 m/s from the edge of a cliff. A stop watch measures the stone's trajectoryg-5.cdolxsdz2yas ht:gi 3(fm:p0ah40gbr 2 time from the top of the cliff to the bottom to be 3.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a r8zv5ofg2wf za)39pubridge. It falls 28 m to the water below. Hfz8 ov23gza )w r5u9pfow far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the grr8:l pt)u8boa ound, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrownro8pual bt:)8?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an anzmr l;h 8s75mogle ofzr5l7 8moshm; $20^{\circ}$ 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 jump krz6nioui5.gro.(o+cne7h i 0l7o6o with a speed of 11 m/s at an angle 6l(5i oo u+ez.cn.i7rknro 0h7oiog6 of $37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launelr4eyh qy;7f,kp( p6ched with an initial velocity of 49.6 m/s at an angle of $48.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocityc2lpn ix gz/.). t2d1xij(isc of 31.9 m/s at an angle of $27.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglehfxt84ihz9e4x.7xr r 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 horpua 71i++ho(eaf6 1 x8fytrq hizontally at 20.1 $m/s$ from the roof of a building 63.1 $m$ 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 speed of 59.9k4+q,*qc t e6o; 4hripei n6ba m/s at an anglihq4;e 4ea *tqb,n p+ 6icr6koe of $45.1^{\circ}$ 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),esa rs.hi3m;elivwrk6- : q :x/ht;g5 you can run a 1500-m race at a velocity of 4.0 m/s. If m x: :righ-qlwevei/;.ts ;63rk5ashyou 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 finish would be

  A plane has an air speed of 200 m/sy:rv 5y. rk-rw due North, and is in a wind of 50.0 m/s to the West. The w5r-y .vy k:rrplane's speed relative to the ground is

  A plane is flying dues2.: c fd6ui ,bb(agbs South ($270^{\circ}$) 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 owhm e-c+msyc +jx1an*4m ) tn1f 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 horizontacwn,j aq15b0; sp d8ghlly fires a projectile with speed 50.0 m/s iq1,bjs 0 ;g apw5dhnc8n 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 8.0 m/s, is directed ac yak9*r9ep ojmv7 d5/qross a river with a current of 6.0 m/s. What is the speed of the boat as it cross5ekod/j pv9 aqym7r *9es the river?

  The driver of a motorboat that can move at 14 m/s in still water wishes to traveaxmhk:t6 gs. c 86noxog*4 ut5l directly across a river 0.9 km wide in which the current flows at 6.2 m/s.ung cox8m6ts5*ot4a. 6 khgx: How long will it take to cross the river?

  The driver of a motorbo-lreflllv.i7fjdik36 le.4 :at that can move at 10 m/s in still water wishes to travel directly across a narrow strait4irl3i.vjdl-e7fllk 6f e :l. in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reamxmw4 t (3sdd/ches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in s xs3d(dwm4t/m till water?

  A swimmer heading directly across a rig*a7w2b 9 q gpa7zgerd9o3wc/ver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstrg7a93 c/ro 9dwawg2zgqe *7p beam 480 m. What is the speed of the current?

  A boat, whose speed e) tcp849dq7jummmv0cxx /da 0ohv+3 in still water is 1.65 m/s, must aim upstream at an angle ofxe/c9v+30 axq4 domm pt8c du7h)0 mvj $28.8^{\circ}$ (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)  $m/s$