Which one of the following 7;.dmzb1slau;i:exyd, esh , is an example of a vector quantity?

  Which of the following operatiol9i1z 8ko4k )n q j+crs(ai8l3byg-q kns will not change a vector?

  Which of the following is an accurate statementxc0vuaj1/ut jk n(p- /?

  The resultant of two vectors is the smallest when the 9 ;gviskqob0iwfh *0th 8b k39angle between them is

  Two displacement vectors na +t9c2yr*o,i,4 rkxb/tltk have magnitudes of 5.0 m and 7.0 m, respectively. When these two v2rytc/tro akt *xb+ kil9,4, nectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the fo,vy * xjvrcm38llowing is a possible answer for the magnitu 3*,8 vjxcyrmvde of the resultant?

  Three forces, each having a magnix2;kc)g bjuj; rm kq1(n055bsqby z *utude of 30 N, pull on an object in directions that k15 (q 2ukr z;jnjsbmx0 yqb)b*5c; guare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vepb48r/k g-qh 8pt1joo )-zjh ector is

  Ignoring air resistance, the horizontal compontvcx ud*7r;9cxmn: q8 ent of a projectile's velocity

  A ball is thrown with a veloci;ey t sd)8jd,wty 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, the horizontal componrj.dr o zg/v18ent of a projectile's acceleration.1 8 /jgzvdrro

  A soccer ball is kicked with a velocity of 25zohcb + .7url9 ylp4lf1:h)c g 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 dire0nwyuv;9dz h;09gzyc 5 aajz4l+c )nscted anti-parallel to the velocity vector,zcz9 l) g9 0nnch4uyavdjw; y s;+0az5

  If the acceleration of an object is always directed perpendicular to its vexe y0 ;s4ld:kecede+-u+*tb qx .xv.r locitx lyc +s eu edvxxq.*eeb.t0rdk:+4;- y,

  At what angle should a water-gun be aimed in order for0vo7kkeqddolipe6 2 ng((. 9 l the water to land with the greatest horizontal rangnl90k iv2q(dl(p 76 eoodekg. e?

  An Olympic athlete throws a javelin at four different angles above the +r(+nl pj3+vs: wekz whorizontal, each with the sa pj+wenl3 +z+rk vs:(wme 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 seconh b/ego04wqlm/4 b5ggzo. 00(j qu bpqd time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizo0/l0gqj405o zqg(u.ghpbem/owq b 4bntal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle o,x,ca mx4qd:i f $35^{\circ}$ 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 o6uyr3ohaz qs;gd 2gs-p.c ;mmj 6 kzkcc /,,/its speed compare to its 6j-gkm/gc;zo3yazru o;mh6k/2 scps,. ,dqc initial speed?

  A stone is thrown horizontally from the top of a tower at thwjl n.xjg1sn0( d kz(zim/.l7e same instant a ball is dropped vertically. Which object is traveling faster when it hits thl/i jsndw17m.l x.z n(gz0k(je level ground below?

  A bullet is fired horizontally, and at the same instan7uzvxst s qvmm 0+x9.u1n3 ge1hfq2u*t a second bullet is dropped from the same height. Ignore air r2 0zf7xs*qum9us13. uhmvg xt+ 1nevqesistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at amo -k5fja 8 3ovqae9e3d-u7 xm speed of 88.6 m/s and at an elevation of 175 m drops a package. 4.5 seconds later it drops a second package. How far apart will the two packages land 93dquokv af3o je8-5m-ema7x on the ground?

  A package of supplies is dropped from a py4tk;4wz1 g2 ie8 yrcxdf)tk1lane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fal8k424)cz igyy;tk1 ftrewx1dling packages will

  A pilot drops a bomb from a plane flying horizontallym( v9a2c9gb cz at a constant speed. Neglecting air rez(9bcvm2c ag9 sistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only on j6x*kw 07e svd:ozs)ke-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you s:jwdv6k*es) 0x o kz7would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis rela7 j doegjja((,tive to a straight, level road and pass a car trg a ((jdejjo,7aveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a riverlu4q7n 0d0vwu that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west4dnuuw 0q0 v7l bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How bs+)u1 wy/yqmz) p go885xhttmuch time will it take you to move 12 km d+b5)1tm)wyx/88p uozh q sgytownstream, in a river flowing at 6.0 km/h?

  Vector A has magnituddrc+(t/o;h(mj l wb8y e 8.0 m at an angle of 30 degrees below the +x axis. The y component ( blyo(d;w+hjc8 rmt/of A is

  If a ball is thrown with a velocity of 25 2xzc6js/m4jni /ak 3xm/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 straigh.ep(x svu 1+ 9cngtt9st line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north oft+ (c1sux 9svepn.t9 g east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vel0fhhq2gb u//n ocity is 8.00 m/s. The angle between the directi/h 0nuf /hgb2qon of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shad,atnk(wb zf /9ow over a level ground. At what angle is the Sun eleva9kafn /,bzw( tted above the horizon?

  Two vectors A and B have components (0, 1) and (-1, -2+kr:vgg5plzun k6, u to-ua3), respectively. What are the componen+n o, uukgu 6zk:v2- a-l5grptts of the sum of these two vectors?

  Two vectors A and B have q0(29d d/ p .cl7vbajpq.xzvf oii49 tcomponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of thesz4fxtv 9pd ov079al iid.(q p2b. jcq/e two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is th ux55dzwyg(/me magnitude5wm/y(dx gz5 u of C ?

  A car travels 20 km West, then 20 km S8xj /0a rq yr94dkxu+mouth. What is the magnitude of its displacemen49xxad8 +ykr/ruqm j0t?

  Three vectors, expressed in Cab9v xxqlay5nv9a* a,3rtesian 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, expressedhn09tzvq+r( 58bk i carb); ee 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 B3btjor5+fut qg q;2a4 = (+3.0, -8.0), what is the magnitude of tj+3u45;2oartqb gf qvector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is/ochw oh jxpsv33 96h5 the displacement of 3 5/hws3x6v ho9jcohpthe jogger?

  Two forces are acting on an object as shown in Fig. below. What is the maiql7 - v+kwqd6gnitude of the resultant fo+6-iw7 vqq dklrce?

  Two forces are actinggle; f9h ci;a2;u 6zzw9vfy 5v on an object as shown in Fig. below. What is the direction of u2 celvig6;f;9 v;wz hf9ay5z the resultant force?

  Vector A is 4.5 cm long and points along the positive x axd*tdnd*wnbj6d/ ,s-pd nh b*0 is. Vector B is 9.5 cm long and -hwnd*6jdd *n, tp0/dns bd b*points at $+28^{\circ}$ 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 78 cm long and points at r)842my /ocxhb b2g qa$30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 39 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)6q mub k*zd-c2/9tw;hx te3xa3f xdy speed of 19 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 3.5 s. What is the height of t3 d* -mthtufzc9dx6x;kx2yeqa/wb3 ) he cliff?

  A girl throws a rock horizontally, with a velocity of 2uv 1 xufbkv94gdtt8oxi7b f7ax i*5:.0 m/s, from a bridge. It falls 26 m to the water below. How far does the rock travel horizonx:xvi 9bufx*4 7fai u7vb.g15 oktdt8tally before striking the water?

  A ball thrown horizontally from a point 23 m above the gr+gz63qzy*6j j6mll z5 ka: gcgound, strikes the ground after traveling hori kzlqca6jz6l 3gm*6gjg :z +5yzontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spe:+ep:gs7fhl red of 12 m/s at an angle oe +fgs:r 7lhp:f $20^{\circ}$ 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 with a speed of 14 ls4rh2 wrne+2m/s at an angle of w2rnsh42 e+rl$15^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 59.3 m/s at an ancaz7r t,oa ):;v 5cbcrgle of $27.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 55.5 m/s at an a j7r*)0blj6yw1y ulbhlrk y m2+ r53ugngle of $25.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle o6itkusg8e)e7dbk r9 2f $30^{\circ}$ 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 20. oh qxt2l4+1dp8 $m/s$ from the roof of a building 64.2 $m$ 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 grounpi(pt:dt nw2 c 2qly32d level with an initial speed of 43.7 m/s at an angwntq( y3c2lpt2p2d :ile of $46.8^{\circ}$ 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 ay,xg vdr7ge jkl;( 8hcn3kdc,z)m05m 1500-m race at a velocity of 4.0 m/s. If you rhl3 rmek75;yczg mk ,n d( ,x8j0gcvd)an 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 wind of 50.0 m/s c1op tics34z)to the West. The plane's speed relati1ptc)4 3zsc oive to the ground is

  A plane is flying due South v b5d(6v;xb:q *x0.wprxnryy($270^{\circ}$) 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 headed/qqjubvt.e o +cbhlu m/ y04ia2k:x,2 $30.0^{\circ}$ 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 horizor0qlj4ql z rbc*9hw a;v *sm76ntally fires a projectile with speed 50.0 m/s in a forward direc0 *l 4b *6qjzm7s9 arwqrchvl;tion $30.0^{\circ}$ 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 rip-ow8rto.ko/ 3 h9xxft; xqb 7ver with a current of 6.0 m/s. What is the speed of the boat as it cros8xkf7q-tx9hr3 t.b o;wop xo/ses the river?

  The driver of a motorboat that can move at 17 m/s in s7ez7um ta+ 6outill water wishes to travel directly across a river 1.6 km wide in which the current flows at 4.5 m/s. How long will it take to cross76 uat zoe7m+u the river?

  The driver of a motorboat that can9vwoh2+a2ubg:h a(vz move at 10 m/s 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 should the driver head the boat?vo9ga +2uw2az hb( :vh

  A swimmer heading directly across a river 200 pftsm/p5akf /z 2 5tg; fyl+:pm wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still:p+ g/ytsp5l2 /apfmfz 5 t;fk water?

  A swimmer heading directly across a ri61ei/x/aqc 2ypeac ) cver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed 2/1) eec c/ 6acaxipqyof the current?

  A boat, whose speed in still water is 2.02 m/s, must ain7w/8:njzqsp )suf / nm upstream at an angle of w/8/n7qsj upn z)n:fs$26.3^{\circ}$ (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)  $m/s$