Which one of the following i;thz27ib sk 1ls an example of a vector quantity?

  Which of the following operations w f9iguw:yaws63j2 b: jill not change a vector?

  Which of the following is an accurat7c(z;qx7 j/ xotjhg3 le statement?

  The resultant of two vecto;m+lwz s(dkw5 rs is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7. od*wbf +bi b4x/p9(ga0 m, respectively. When these two vectors are added, the magnwdaf xbgo pi9b *(4+b/itude of the sum

  Two vectors, of magnitudes 20 and 50, are* yufwky bel)h 94y6lfi kw.;zw2u7 8v added. Which one of the following is a possible answer for the magnitudee4ykw yllhz.9;)fui*2fw7 wyv k8 6bu of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in .d+ruiqnsc c d9 x29vs.q(*b sdirections thanq+cxid.bsq*2us dr 9 .v(9 sct are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the un50s;0 mz nm2luvhyjd 4known vector is

  Ignoring air resistance, the horizontal componendtps2uzhc *1hc 0x md;zz+1 d,t of a projectile's velocity

  A ball is thrown with a velocity of 20 m/si4fhygvhx,qm4b m4hu/ m2xb0o27 eu0 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 resistancj xmm7 v*ibt4 b2s97g.f4y wmye, the horizontal component of a projectile's accelerationw 4 vigt9y7y*bmsm. fbx4mj27

  A soccer ball is kicked with ; tqfe:gvqn3./d6; lbhzp1coa 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 rzg o(z; zn)4nvelocity vez; zn4)( zrognctor,

  If the acceleration of an object is always directed perpeu0g0nj+6ag jkq y s8 0zm4hmi,: vq8lbndicular to its velocityuym n ,l0qg s4kvb8+80aqmz6hjgj :0 i,

  At what angle should twn)1j37tkf v kik / . hp-i-g+x9ffwua water-gun be aimed in order for the water to land with the greatesfhx -- f7 kni1tuk.wpw tij9 gvf+3/k)t horizontal range?

  An Olympic athlete thro/i6vq5pcjuvsz, pf f.:8 ;t .m5 pteucws a javelin at four different angles above the horizontal, eac5csi vuf/vpe68,tq pcf jm;zt : .pu.5h 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 the second time. If the)v*c)ys js11/rn yile ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R )iny 1v s y/sle1*cr)j(compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s a -s8 t5ok99qgafaxst(c (t+ jmt 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, how does n mvq:) ihuhy; )k4kx/its speed comnu4v )/x h:)kkh qymi;pare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same sj,v: wxnh:+f instant a ball is dropped vertically. Which object is trav+hvx ,f :wnj:seling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same inr- p z:8mirb0k zjs3(kstant a second bullet is dropped from the same height. Ignore air resistance. Compare t-rbizr zk0 3spm( 8k:jhe times of fall of the two bullets.

  A plane flying horizontally at a speed of 118.2 m/s and at z0 yrkme m/+ 6v./yiwvan elevation of 219 m drops a package. 6.8 seconds later it drops a second package. How far apart will t i0/e myv6zk.yrmwv+/he two packages land on the ground?

  A package of supplies is* p /ssuul0:l.i )nmoy dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the :yi0/ l*.u n lp)smsoufalling packages will

  A pilot drops a bomb from a plane flying howo*ps69,x+n;jn jnq 3w fkb3 urizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location ofx,jnk;n9 u63wjb*f+qnw s3po the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth.f h465as bzc( std73bb If you hit a baseball on the Moon with the same effort (and at the speed and angle) thats 3sbd5f(cbha6zt 4b7 you would on Earth, the ball would land

  You are traveling at 55 mi/h in t g2,s) vwr4wvshe +x axis relative to a straight, level road and pass a car traveling)4 2gwvss r,wv at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flof/dwqxhewm*1a : r,c piz- 91nws due south with a strong current. You start out in you1 ic whnmzfp1*wxe9-arq/,:d r motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How ws :px4,xv rbe0 -i+njmuch time will it take you to move 12 km dow:njbx spxw-r0e v+i,4 nstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an an .bkn(-1ks/4lf v a/u pjncqm2gle of 30 degrees below the +x axis. The y comp2flb4s-/.pn/ u qckj1( nkvma onent of A is

  If a ball is thrown with pbe.n -as -qgmg6; 8dsa 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 ofdiz/g+092 xqmxwn) ;sn/xxz u east and you end up 2.0 km north and several kilometers east. How many degrees north of e nx);ux 9s/x0zidxzn/g+qwm2 ast have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity isui5ifl 7xg p64 8.00 m/s. The angle between the direction of its mgl4i 7xui6f5p otion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow ove catjh-6f7dkb1e0b c30c jf l4r a level ground. At what angle is the Sun elev fldc-bbk 6j 1h7ta 0je4cc30fated above the horizon?

  Two vectors A and B have components (0, 1) and (-p z6s2zsh5z +n1, 3), respectively. What are the components oz +s52sphznz 6f the sum of these two vectors?

  Two vectors A and B have componenta(swg0 o0:d t.i+ t22yauiilks (0, 1) and (-1, 3), respectively. What is magnitude of the sum of the+t(. o0ta s20di2liyik a:guwse two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What it44:g sc 2n7dv x.h/otvh0 fritsmp0 -s the magnitudhvdp m4n .c7/stsi-f t0hv 2:t0rog4x e of C ?

  A car travels 20 km West, then 20 km South. What is gqwgjks ,45 z6the magnitude of its displacement4jqz6sgwkg ,5?

  Three vectors, expressed in Cartesian v hzakrbk3svj78e+) m - 6;vijcoordinates, 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 Cartesiauoub ;g5kom2f0me ((jn 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 vectokabh *5po7 m/pr B = (+3.0, -8.0), what is the magnitude of vector C = A - B mah 75bpo*/kp?

  A runner runs halfway around a circular path of radius 10 m. What is txfhu0rv z*+i 5grb+ h,he displacement of 0f+ux,bhiz+h5g *rvr the jogger?

  Two forces are acting on an object as+ (38va8tirgtapcx vlt +8 :pj4rjcv1 shown in Fig. below. What is the magnitude of the resultant force?p:8 1v8t i x jjtvva3(lap+8+rcrcgt4

  Two forces are acting on an objs3p )ros w*2z .hph0zzect as shown in Fig. below. What is the direction of the resuz 3wh r.z)p*20oss hzpltant force?

  Vector A is 3.5 cm long and points along the positiv1xv uc8+f6s4a2 s ) qcptiex)re x axis. Vector B is 7.6 c f)qpuv1sx8+ x 46c)2irc atesm long and points at $+30^{\circ}$ 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 points at jq * z0u657dt)qcwx8.: )ucyedekgso$30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 28 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 w6r z.7lxtg l((v;nzpwith 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 the zzxn ;(g .v(t wlrp7l6cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocityz lad*vsc +k16fx2 j1r of 5 m/s, from a bridge. It falls 12 m to the water below. How far does the rock travel horizontally before strik2*kcadj1fz1v r sl6+xing the water?

  A ball thrown horizontally from a point 25 m above the grou .8ap 6pijsbvcg-n0 *ynd, strikes the ground after traveling horizontally a distance of 23 m.6*sjbya v0 n-c.8pigp With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of(m4 ci1sbpv5 w 12 m/s at an angle ofbiv4p51 wsmc( $20^{\circ}$ 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 jui 7crfq-e- n9smp with a speed of 15 m/s at an angle o9s ecn7 q--firf $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 20.7 m/s at an 1s;z b9xn3s(b*gs uorw(2 g;ctd9qc gangle of $17.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 46.5 m/s at an71wxaoaj ,m4 a angle of $21.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of tzo:z6f0 nuv :$30^{\circ}$ 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 horizontalle4 tb(u .ku0qt6cy5n my at 17.3 $m/s$ from the roof of a building 56.7 $m$ 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 gru//4m((i cdi ea.gikqound level with an initial speed of 50.1 m/s at an angle o (gi/d kiq(uc.mi ae4/f $41.9^{\circ}$ 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 1500-m race at a velocity of 4.0 m :i)fb -jo ;es3thk wj9l2m/dv/s. If yo9fev)w/lo -js32 mhjb: ; dtkiu 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/s due North, and is in a moypgp nru:j 1k 13-vm:;sf(i6mc -pswind of 50.0 m/s to the West. The pm -yiu3vo r1mp1: -s:6fnjcmskpp g(;lane's speed relative to the ground is

  A plane is flying due Southj-x qo/ .0/lrdn i:jwfg-; 9cool ;sjv ($270^{\circ}$) 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 l(0mc0v8gt x02up nrwis 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 hog8,p.zhwii+h bf qd(ywl f+d5 +0hvp+ rizontally fires a projectile with speed 50.0 m/s in a f5+ yz. q +dhi8+ipl(g vwfdbp0+ hw,fhorward 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;; 22dtb2bynlop0gdjm4q) xy n+ayq4 km k7e7 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat a 7m p njkk4; ;y422q de0taq2yblnmg) xy+do7bs it crosses the river?

  The driver of a motorboat that can move at 19 m/s in sto 2r1p 31lgqiyill water wishes to travel directly across a river 1.2 km wide in which the current flows at 5.6 m/s. How long will ig2l yp qi31ro1t take to cross the river?

  The driver of a motorboat tja;px/obgj u+k d0-q3 hat can move at 10 m/s in still water wishes to travel directly across a narrow strait-3 b;gj oqudxja+/0 pk 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 reaches the opposite bht0 yfxt4w+fyc.pj48 ank in 6 min 40 s. She is swept downst +0y.hy c ff84t4wptjxream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the pi/s/):khbz:ip a e 2oopposite bank in 6 min 40 s. She is swept doa//: i khesppb z)i:2ownstream 480 m. What is the speed of the current?

  A boat, whose speed in still water i4 flp tsviht6p9 :(os3s 2.08 m/s, must aim upstream at an angle ofl :fovph( i46 ps3tt9s $24.2^{\circ}$ (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)  $m/s$