Which one of the folloby* 9*n9q t 3l8 wwe5vofupt*ywing is an example of a vector quantity?

  Which of the following operations will not chaaa/ya58 5 vd r8rnrpn x-iqq(lpy x7((nge a vector?

  Which of the following l (q+:nf ffah8evxm36is an accurate statement?

  The resultant of two vectors is the smallest when the angle betwee i(*nragl0 )fxn them is

  Two displacement vectors have magnitudes of 5.0 m and 7.tx,qo734 k n 3g/v7k5phlwybays 4*ev0 m, respectively. When thesp a l34*/yt7, kvh53wvgsyb oen4xq7ke two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added.se *jp 5w7.67fz9qoty suxjedl+ :d9u Which one of the following is a 6fwq uljo7dy7j9uzdp e9 x e.5*+sst:possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direct-c b:+yl3qi.1( m gaztrkcbr 3ions that r-zk3:ycmbrt+al(.b iqc 1 3g are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknzv0 n .2dgod*ay5nf6hown vector is

  Ignoring air resistance, the horizontal co16r1- in3pkb bn(s qs0avm +wf/jh9ca mponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle onzoq:c se+ )5ewm-hk;f $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizon73s -u me0m8vrluxzv2tal component of a projectile's accelerationxm vl2vz8s3- mur07 eu

  A soccer ball is kicked wiwaow6k4*da j.nv-y +lth 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 oxj k7f4njrkh9s mu1zm5u- oa q//cm4 )bject is directed anti-parallel to the velocity veczhx/74 a u)m cjur1om- fmqjs k/nk594tor,

  If the acceleration of an object is always directed perpeejfd+b9d vatin ( - irv7ey.0*ndicular to its velocittf evv9eb7i*r.n yj +aid0-(dy,

  At what angle should a water-gun be aimed in order, lgk ++teibll785x ge for the water to land with the greatest horizontal t8 be5+g7lg xiell, +krange?

  An Olympic athlete throws a javd brz6: 75jkpielin at four different angles above the horizontal, each with thz jr 7pbki65:de 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 bzg3 2 gpu v41pac*cf27i1xxik all for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared vz7f*3c41aupck g g ipx 122xito your first serve) would be

  A ball is thrown at an origrni;a+ /h pqu -y0 eyzz2 is2/fh*goyaoj)j,.inal speed of 8.0 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 field goal attempt resoitc0fe5c o mub-,hd b7-f, 5aches its maximum height, how does its speed compare to its initii,7 ct5b,fue50h-sm c bo-dofal speed?

  A stone is thrown horizontally from th * yo/k1ayew/.yvy*lc e top of a tower at the same instant a ball is dropped very l /v.cykywe ay**1o/tically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullev cf 8,f2l, xa3s6g2trj t8ncmph f)z;t is dropped from the same height. Ignore air resistance. Compare the tima2,r6ft v8xf3,gpz t js8l)2 hcncf ;mes of fall of the two bullets.

  A plane flying horizontally at a spvv,4-iy 8 wul76 ksfsweed of 56.3 m/s and at an elevation of 123 m drops a package. 7.6 seconds ki6fu-8 7,ssvw4y lvw 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 px6e7;( lli lpnlane, and one second later a second package is dropped. Neglecting air resistance,ll l67x(eip;n the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizoh9(.19qn ej s0axw dgj2x 6yajntally at a constant speed. Neglecting air resistance, whe9w1q (yjdjn09.x6e gs j2haxan the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that onmd: )7u 2g/+av5ydocw sxbq4k5nfg,n Earth. If you hit a baseball on the Moon with the same effort (and at the speed a,:md byf gdq5w2sn)+cgv5n 7xoa /4uknd angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the6xd0icop6r t,uw 1.ka +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your cu d t01c,.o6karxp w6iar to the other car is

  You are trying to cross a river that flows due s6qvnm)amm6gt .d p )(eouth with a strong current. You start out in yod(.6n gapmm )m 6tqve)ur 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 kmdzmw0mkz(.v gr;6:mv:6a04wsy mzl o /h in still water. How much time will it take you to move 12 km downstream, in a river fz( .g;6l4 z sm amwov0 d6:mky:vmz0wrlowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 3066dm gl;evu,dk otwjr 9..z g; degrees below the +x axis. The y componu .;rzlo, 6;.6jmkgtegwv 9ddent of A is

  If a ball is thrown with asl3nmsng/ab7 yb *,ceypx(8d 7( -ftf 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 direct6il5p xb(dl 1sion north of east and you end u(l pd1i5 6lxbsp 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a spee5d knnc-jsxid4q b) )(d of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its mq-(ndxkjc)is b) 45dn otion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow ovej,oyqztc c6au0y)3 o( r a level ground. At what angle is the Sun elevated above tho(yuc,6c 3jq)o zayt0e horizon?

  Two vectors A and B have components (0, 1) and (2rf vlaso;i-lk9l; zhw7l /)z-1, 3), respectively. What are the components; ak9/2hf7v zw lro-lisz;ll) of the sum of these two vectors?

  Two vectors A and B3u;xt0 -1r zn,h 7uyjqu fecj/;kffg) have components (0, 1) and (-1, 3), respectively. What is magnitude of the j;y ;1hut/cfx-uj,)enz gf q k07ufr3 sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector Cjr:m5jp82)yv78+rxf o fp lt j = A + B . What is the magnitude of Cx)o5jjff rt mp8l8 72rpj+ vy: ?

  A car travels 20 km West, then 20 km South. What iu1cw31,sooo9qnpr h6s the magnitude of its displacement sp crqoow1h3o9nu,16?

  Three vectors, expressed in Cartesian 5mdbb 484rt8o9f wqoicoordinates, 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, express-xyj .pt4l*w4 qo/fw-afsg1 b ed 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) an*nm; nss ;d6co qn)d2 rvjz8w5d vector B = (+3.0, -8.0), what is the magnitude of vector C = A -so5j)d ndm 2 qc*rn sz;w6nv;8 B ?

  A runner runs halfway around a circular path of radius 10 m. What szm*qm 5cd( f5 .vxfv9is the displacemezf5s. fq5 v (9*cdxvmmnt of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is t.f3/hum z::hs) ac )dhl d pydl*o45huhe magnitude ofm))3 u hdhd*o/cpu:alh 5l sfhy4z.d: the resultant force?

  Two forces are acting on an object as shown in Fig. below. What isg7+2w1 ;4 q1 symer4 kzvwt)jcyv3ihh the direction of tht;j7)ygkwq1 w mev4+h1 3i zrshyv2 4ce resultant force?

  Vector A is 4.1 cm long and points along the positive x axis. Vector B kwv2zxm*wu;u. oc tp1(cin - 3is 8.2 cm long and points a(tzu23wxv - ick n*pu1m;cwo.t $+32^{\circ}$ 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 85 cm long sy2zt w8tb7i11.b, t5 aaesf aand points at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 45 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 wit 0(etm.(he fit 0ggbw:h an initial speed of 22 m/s from the edge of a cliff. A stop watch measures the stone's trajectory tim. 0 wtmbi:(e (0fgthege from the top of the cliff to the bottom to be 4.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, from a,w lfh r7/wc-b bridge. It falls 29 m t w hb/wlc7r,f-o the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the gr,3n:5f7e5 13sop rzvhb yl pdc- ihf-vound, strikes the ground after traveling horizc iepb-hv1drh:37n-l p5fv3 ,soyz5fontally a distance of 12 m. With what speed was it thrown?

  A jumper in the long-jump gdrlq ipr2; 3i) m99iy7rusqa9 oes into the jump with a speed of 12 m/s at an angle of d;r9qpr 7i9q 3i9 i2)lrusy ma$20^{\circ}$ 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 13 m/i8g l6o ;hgy0t j1.vtvs at an angle of v.0 jtgl;go86i h1y tv$31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 52.7 m/s at an angl2:d z83o;z* mctr gpfze of $42.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 39.9 m/s at an h e t6fy c3wh z2z1aamalu8lk06b 0(m-angle of $30.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang(ik19ql svx*oz: 2*t yxuh2xq le 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 horz4k:e2deu r 3ry-l xz38cuxj9izontally at 21.3 $m/s$ from the roof of a building 47.4 $m$ 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 kqlah *uk(ybt(r g,;. initial speed of 44.6 m/s at an anglb,g kk*rl;yh uq((t .ae of $48.0^{\circ}$ 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 runr-8lt.t+ a rrz 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 which slows your speed by 2.0 m/s, the time it would take you to finish would. +tztra-rl8r be

  A plane has an air speed of 200 m/s due North, and is i/*y pkcli0h,zpc+ i 0mn a wind of 50.0 m/s to the West. The plane'sk+iim /zhc, *yclp 0p0 speed relative to the ground is

  A plane is flying due Southxs 1a4a6/oi mkfcr15 h8rg) dx ($270^{\circ}$) 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 k qk1f yz:cey op++d9s;m/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 iul*om+n-cw/)u,vzpnpl7 8c fires a projectile with speed 50.0 m/s in a forw 7nzcl+lu8/ucw i,om *-v)pp nard 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 f*sa5nq ar1( hrth -4fwith a current of 6.0 m/s. What is the speed of the boat as it crosse(h -ha1rfns 5rfaq4t*s the river?

  The driver of a motorboat that can move at 16 m/s in still wa:/ 6 ,c1u9zi sriefpvfter wishes to travel directly across a river 0.6 km wide in which the current flows at 4.3 m/s. How long will6pffc19r u,se i i:zv/ it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wvp* av/mi9 cx4)q7lln se1n v0ishes to travencsm/ 7 *iql)na 4epxvv 0v9l1l 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?

  A swimmer heading directly across a river 200 m wide reaches ek8y36nv(f a px)bw8 vthe opposite bank in 6 min 40 s. She is swept downstream 480 m. H k3x epy(f8bw8avvn6 )ow fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite band8sw5b6et8w rj*b:m5nl0c kn zzb+lm- 9 sv0dk in 6 min 40 s. She is swept dow88es bzd kmbct* sm0-+ 9wbnl0rv dj556wzn :lnstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.06 m/s, must aim upstream at an ang x(6bjsac sj,4le of 46(,jj sxbs ca$24.7^{\circ}$ (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)  $m/s$