Which one of the following is an exam q)xd il.g pa;s;95actple of a vector quantity?

  Which of the following operations will not chtx(j4az 8m1ur -1et hq;;euqf ange a vector?

  Which of the following is an accura l0e px5u);jb gtf 3uup-q57a0e+aiagte statement?

  The resultant of two vectors is the sa .y2qh0w7p8dl v4hqfn6pd*z mallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respec, eeakk6 re8-rtively. When these two vecr,86rea-kkee tors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whicm0tz4dt3n.)rnq qs z8h one of the following is a possible answer for the magnitude of the resun38.szzmtdq ) rt0 4qnltant?

  Three forces, each having a magnitudes(,qlci7 u..u m 6hfo,,nmwoh of 30 N, pull on an object in directions thatmu7. l.mufw soo qc(inhh, ,,6 are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the un/kmz e;8mjy0ry zi2a3 known vector is

  Ignoring air resistance, the+3l:.uqbhvm5my j o.wyl ; 1jw7mkli- horizontal component of a projectile's velocity

  A ball is thrown with a velocity o;sjegiy4m4 mo en a.-)f 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 hori4n6qf vk (ww/k87czk 8sn;ikkzontal component of a projectile's accelerationn78 w qknkvfswi 468kkk z(;/c

  A soccer ball is kick qug39sx6qm ).6eookf ed with 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 z h92 z+/tj9h.( i- iff; cuoute5cugcvelocityiuutz+-fe(c9cf5h t2j /;ig ozc .9uh vector,

  If the acceleration o(77h + i*pe l;em/if+poltpt2;s ny wqf an object is always directed perpendicular to its velocitywt hi l+y* fpt;/pp27 7e;nisq( mloe+,

  At what angle should a water-gun be aimed in order for the water to la-qfd. ux rfp)1nd with the greatest horizontaf)u 1xrf q-pd.l range?

  An Olympic athlete throws a javelin at four different anb ag1x ep0.l4vgles above the horizontal, each with the sa1.e g 0xab4plvme 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. b(ztjnm1bx 7sdz6++ gIf the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would b s(z 1+7z +mbdjnbg6xte

  A ball is thrown at an original speed of 8.0 m/s at an m k.c1c:yda -d -k d5c,m(agwkangle 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 gnjj:+p eib ug90 v74zdoes its speed c g je0bpzu+gni:vj947ompare to its initial speed?

  A stone is thrown horizont oocf ;5 jfkz+(lsuj5u(bcwoyu . :a;+ally from the top of a tower at the same instant a ball is dropped vertically. Which object is travelingfljy;c( b sou:c +oj+a.(kwz5ofu5u ; faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dro+g;:y:u;pxqzb) nb icqojn0 1pped from ;uqjg0bzp n)1c::n+x; y oibq the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontj-*1ze2j,maksnnh;hioc d 2 gr 3ep. 5ally at a speed of 42.1 m/s and at an elevation of 183 m drops a package. 6.0 seconds later it drops a second package. How far apart will the two packages land on the ncjn,2 mkrg eh*53d1si. azepoh;2-j ground?

  A package of supplies is dropped from 9.j1(o*arzn7el.3 dhtzyh(cnw+qbj a plane, and one second later a second package is dropped. Neglecting air resistance, the distance betweeqbjh.*hzn z yoj(7w1t9a rc (+n eld.3n the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Nx88;,vgf dgfqf x*f e3eglecting air resistance, when the bomb hits the ground the horizontal location of the plane willff*,fx;ggq dvxe3 f 88

  The acceleration of gravity on the Moon is only one-sixth of that onmpea/2m (4k b1 um8(ajxqaw.s Earth. If you hit a baseball on the Moon with the same efmeak4q(1 w(bs/jmxuamp a .82fort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h ix.kikr.oj( e9s k7ww:n the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocio k(ie7kkx:w. w9.jsrty of your car to the other car is

  You are trying to croskrcqk o 0/1qs:g9-oz ss a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. Yo0 c1qsg:oqk9/skzor- u should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it takged0e1*a1) okt u 5.vcbh8/0xyzgguue you to move 12 km downstream, in a river flowing at 6.0 km/h0u0 g18ek xbtgvz 1gu5 /h )oecudy*a.?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. Thd6(+ 8k:0bmbwgx0;wd,jjxx y nw)olke y component of wog:d k+yn0)x 6jjbbw;l x,d8mk 0w( xA is

  If a ball is thrown with a velocity of 25 m gym8f;jqbtq 41qqd+k36l dr z8bf6( 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 direcuqk/: tnu9v :rf vh+tw3- br zue/0mz8tion north of east and you end up 2.0 km north and several kilometers east. How many degrees :9/tq+fu zek-v 8 0hrv3 b:umwtu/rzn north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of itsf )krvcydqv+t.fx;)5 nhy :y; velocity is 8.00 m/s. The angle between the direction of itnxt 5)kcf;v rf d:yq)h;.vyy+ s motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angs3f)ez3edz5 eyq/t- d le is tf-5y33/ eedzes q td)zhe Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and .no /nn9xt8ipfo(nu 6(-1, 3), respectively. What are th8un i/otof( .xnn9p6ne components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respv6j k7dsa m36lko:;)qj rdyo)ectively. What is magnitude ;ls j3d76qojd v)k6k)ra:my oof the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vr4/d kyt; ntxq*;u4jbector C = A + B . What is the magnitude 4ut4t xrjq ; *db;ny/kof C ?

  A car travels 20 km Wesfr(ec(8b r.qxt, then 20 km South. What is the magnitude of its displacement?f(.c qr(r8b xe

  Three vectors, expressed in Cartesian coordinates,7wtlp;i, *+f7gfgnz ezlh. (i 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 coordinew ocf,y5d,5 ,8 0qwk zzjmro3/gwp6bates, 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 = (+3.0j5)ws)*flgs m , -8.0), what is the magnitude of vecmlfs )g5ws )*jtor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. .5nn xpfv5-biwa dm9 j(hye/6What is the displacement ofmdj9e 5n.vx-6 h(fwiy5 nb/ap the jogger?

  Two forces are acting idvybwr6y h9/ /2kq .xon an object as shown in Fig. below. What is the magnitude o6d/ / r9ivq xwkyhyb.2f the resultant force?

  Two forces are acting r+o26(tqy0d lqkq ;clon an object as shown in Fig. below. What is the direction of the resultant forky dl6c(qo;+rt l q2q0ce?

  Vector A is 5.8 cm long and points alongsyr 8f4y k.xyno,p2 a2 the positive x axis. Vector B is 6.1 cm long and fs, r pa2 konyy42y8x.points at $+47^{\circ}$ 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 63 cm long and points*s5 (wsffthj, at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 34 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 speed of 12 m/s from the eyg/1htmq; it 5dge of a cliff. A stop watch measures the stone's trajectory time from theq imtt;y/ gh15 top of the cliff to the bottom to be 5.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a bridge. Igh dt 27 uku/:jyf 5hc6otm88;emzax4t falls 11 m to the water j4fh e6c azykumt/88dm g7uox 5;th2: below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 m above the groundy9 w- .,f)j2oc+gnb 1q3v-qq ikftcaq, strikes the ground aftb-qwyqvg1)2 t9i, k jof-f+.3cqcqaner traveling horizontally a distance of 15 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a rw* 7rdj68zv r6gc.vth )qde j 3+pdm/speed of 12 m/s at an angle of +gr66hzd cw qd 8dj)et vr/.mv*7r jp3$20^{\circ}$ 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 sbndusacr9f 35 z8-/6u t;mqnspeed of 10 m/s at an angle osbscu;u 6d9t/ a-n8 5z3 nmrqff $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an i5 mgjsm8mkmtj*k0dhn:kt x1b.v).+ fnitial velocity of 34.3 m/s at an angle of $12.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 39.4 m/s at an angle of /qtct(pn9x8 o$26.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an-o t;fyot8j v)gle 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 horizontallypjnqx5c.r b /x::b(yd at 27.3 $m/s$ from the roof of a building 60.9 $m$ 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 initial speed of 64.6 m/s at anp w5y9kqs:v 5a wyqak9vs 55 :pangle of $40.9^{\circ}$ 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/s.w/ z s0b.aqn;;yyfut vm+)i7n If you ran the sammb/t 7q;+0s) ;yzyfaniuw.nve 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 :ncl,3m1 v/vkt*5*bk s bef yuis in a wind of 50.0 m/s to the West. The plane's speed reb3b**k,f s1y5v v:ceknult/ mlative to the ground is

  A plane is flying due South )s brsbjt;(oqfjj/pb7n; k qrl(2n-hq 0 : fr-($270^{\circ}$) 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+15dn gs gu)2j0gvonmfj +*ip 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 prh4-y6ubfa g0lgjo - a;ojectile with speed 50.0 m/s in a y4aggj-0lh -6b;ufo 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 wud6-aka g)4 s+,fwtvvih::k b ater is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosse,-a hwafdukvkvt64g )i+ b ::ss the river?

  The driver of a motorboat that can move at 9 m/s in still water wisd fyt5)i*l6k8+jrllz hes to travel direitrj56z*d)f8 +kll y lctly across a river 1.6 km wide in which the current flows at 6.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s vd1)t3s g9q9ko 3wpsnin 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 bo3 sd13no)kqs9 tw9p vgat?

  A swimmer heading directly across a river 200 m wide reaches m2zzpr9g8 mpe9g* ln4 +2ucz athe opposite bank in 6 min 40 s. She is swept downstream 480 m+*l2z 2umezapm r9gng 8z4 pc9. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m widevmvto,;v 6lq htjf.1 ( reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the o.1vh tv;jftlqmv 6 (,current?

  A boat, whose speed in still water is 1.40 m/s, must aim upstrewz 17 b0qo,ed8a nkzm5am at an angle ofazwobme 5 nk7q81d,z0 $16.8^{\circ}$ (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)  $m/s$