Which one of the following is an example of a velz(m z:v5icc7sv;nu) ctor quantity?

  Which of the following operations will notupzn xxn/a, kc1 +7(yk change a vector?

  Which of the following is an accurate sypl7697 xa09a pvj4kfr- kpqstatement?

  The resultant of two vectors is the smallest when the angle betwee+h 6*xvx /pnuxm m-r.mn them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. v6hbv9wkabts u ) v*j8nt;1 n7When these two vectors are added, the magnitude of th a9 t8jw)*vtnh7b6vv;1 knbuse sum

  Two vectors, of magnitudes 20 and 50, are added. Which onepdi u *k/6u.y/mnrd-x of the following is a possible ny /pxdk6i.-ru/ udm*answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dhyx0 1z sn*-hbirections th- 1*0bxszhnh yat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector ryw 2jaai7v30 is

  Ignoring air resistance, thege i-f 7iknu,k.udaq j6y7b: q1t5to 3 horizontal component of a projectile's velocity

  A ball is thrown wite26 hxij2)h cqh a velocity 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 component of a projectile's acceler ;p:g4y:a 2kflx(l wugation xy afg;2wulk4gl:p:(

  A soccer ball is kicked with a velocity of 25 m/s at an qg- vj5q5 in wh ,6o4ptg1izo*bwn6;m 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 directta9 7uk.v7kl wed anti-parallel to the velocity vector,k.kvu7 w7lat9

  If the acceleration of an object is alwaysm; ukhgh8m+lc8( u6 fj directed perpendicular to its velocity;8hmug8jflh +6(uk cm,

  At what angle should a water-gun be aimed in order for the water to l6 w c21-yleopucg2m *xand with the greatest horizontal ranul x6y1e2owgc pc*-2mge?

  An Olympic athlete throws a javeloa qz9,3 rwc(p vcdv1:in at four different angles above the horizontal v: aw1,zcvod3cq(9 pr, each 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 bu ))(q)qvway* ft- fzqg4zz*j 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 (com)zqq4y*utqf)*wj ( -gv) fzazpared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angv+)gf* n:d)rng cp q)rle 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 attemp( +s)5l(ce/ce- 4fk wexi spamt reaches its maximum height, how does its speed compare to its inxskef w eal-m5 )(sc+/pe i4c(itial speed?

  A stone is thrown horizontally from the top of a tower at lw9:z i0s kdy.the same instant a ball is dropped vertically. Which object is traveling faster when ws90zl.dy: k iit hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dr5 i*oy77uw9ey8 ;c. +mdl1 jh tsffkksopped from the same height. Ignore air resistance. Compare the times of fall of the two bullcj 9k+17m;yw kie sfuy7t dhosf.l8*5 ets.

  A plane flying horizontally at a speed of 88.0 m/s and at an elevation of 298 m uidox56)4gy zyj,l p-drops a package. 3.4 seconds later it drops a second package. How far apart will the two packages land on t)i oluy65y ,-p zjxg4dhe ground?

  A package of supplies is dropped fromvb7*yk o;isjxs.9 2 bvms fi9:t1s2p i a plane, and one second later a second package is dropi*tiv2sbsb yp99xo i;s2m: fs .k17 vjped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a tj.c )z-m qdw2plane flying horizontally at a constant speed. Neglecting air resic2mz)w.tjq- dstance, when 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 on Earth. v4q 8:z5rto-wgnr ,ii If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball, tnri wro-v5z4i8gq: would land

  You are traveling at 55 mi/h in the +x axis relativzl0*vc: +vkt ye to a straight, level road and pass a car traveling at 45 mi/h.:yl +*kvcztv0 The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong curgrs4cc;m(/ 5*6fhx 6 tjabr arrent. You start out in your motorboat on the east bank desiring to reach the west bank directly west 6 x4/r;h rsrf5mg aba(cjc*t6from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How mugzvq;i4 by b.l08 d)a;rh(yiykk96tf ch time will it take you to move 12 km downstream,r a(4hklb)id0 qkbt9g y;68;.fvyziy in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m vhk p r-w8c7qli3ro-w0is9j,at an angle of 30 degrees below the +x axis. The y component of Akp-ivlw8s rh- 37 rwoqij, c09 is

  If a ball is thrown with a velocity of 25 m/s at aa6(6h v2 vknson angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight li-hv n:a96)f hwlf f0fhne in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east havh0wh9-ff:a nf l vf)h6e you walked?

  A butterfly moves with a sk/:me/a (ob ov5frvfsv13 gt9 peed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must bvt f/ 9( aes3orfog vbm5v/k:1e

  A 400-m tall tower casts a 60o 7 xg2oj 8vr* n3zv v2uw7v5o-nqt2pr0-m long shadow over a level ground. At what angle is the Sun elevated above xno zov2wgq n ovv827trpr27-ujv *53 the horizon?

  Two vectors A and B have cx yzvgguip2)+u 1ex*; 5vu 2pfomponents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two vectors? uv+2*2exx pzu )gygvi15p;fu

  Two vectors A and B have comp6ox6qe2cptv gf12y 1iz la*ss(*u0 psonents (0, 1) and (-1, 3), respectively. What is magnitude of the sum (p*g626e*t 2auoz1p xyqscils01svfof these two vectors?

  Vector A = (1, 3). Vector B = (3, 0jb2 wkya32 (cqqt p6:l). Vector C = A + B . What is the magnitudebpk qq:(62tla wyc 3j2 of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude oeo fi,wyl7jz4 5z6ve9f its displaf75i jy64 wv zlo,eze9cement?

  Three vectors, expreom (-4x(kmez issed in Cartesian 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 cooru8 uumc2 1e)jur pp6 7 y5gpp1u:ubje9dinates, 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 = (+3.0, -8.0), whatmt7f4fh a(4 fkh dy+h9 is the magnitude of vector C = A - B 9mfy4f7 k h4th+fahd(?

  A runner runs halfway around a circular path of radiu0f p(8(a tuxdny mdfijl/-p7yq*49 g rs 10 m. What is the displacnjyitpq dfx -ld 87 (mfyu*a4/g(rp09ement of the jogger?

  Two forces are acting on a/+g2 sbmcx3; gzyrbw3n object as shown in Fig. below. What is the magnitudew/m +2g;3brc gs3xyzb of the resultant force?

  Two forces are acting on an object as shown in Fig. below. Wz(uf e;sgj s m38kdik6g,3zd3hat is the direction of the resultant force?jsz383ezmgk,u6 sfg(3 d d;ik

  Vector A is 4.5 cm long and points along the positive x axis. Vector B is td(+ (g+n ;(-)g2zwo utwnmm*ytnaig 9.0 cm long a au tgwo*;mz-++t gnw(2t (y(mgn)dinnd points at $+42^{\circ}$ 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 71 cm long and poiq+pn.gmoy wm*9vb3i,3v tr5cnts at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 38 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 27 m/s from the ec):pdx sr 31 k qaylo40w19iiuipeq..wov72 vdge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.6 s. What is the hek1uvp.)i0:p wi iv or wx12c3q7.yeasq 4ldo9ight of the cliff?

  A girl throws a rock horizontally, with a velocity of 20 m/s, from a bridge. (,s,vb3 eodf 7gh01q;kc-y(rgz mocaIt falls 20 m to the water below. How far does the rock travel horizontally before strikiq(gfcbe ,c0rh s(y -, govdk 7;ma3oz1ng the water?

  A ball thrown horizontally from a point 24 m above the ground, stra+t 5f xp6j 9m5dqgv;xpe29wpikes the ground after traveling horizontally a distance of 22 m. With what speed was it thrown9;2 vgfd+ ewq96pxpt 5pa5 mjx?

  A jumper in the long-jump goes into the jump with a speedwlcq8pv 17 y6k0 zfcr* of 12 m/s at an angle of 6zrfp8 c*v7 1kwlc0qy$20^{\circ}$ 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 ws(j *(lz 5bmhybp hq8*ith a speed of 13 m/s at an angle of qmzlsbj8(hp(5h*yb * $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launch-jx i;yfdw0* 0 fqtr z-+ug,hj 4zehu/ed with an initial velocity of 45.4 m/s at an angle of $16.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 56.8 m/s at anh:4jkqzx rer gnh*(3 / angle of $14.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of mdf*ib; b me +lo/8bk1$30^{\circ}$ 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 cv;io g ut:jmw n3b;v8,yc c*)at 16.1 $m/s$ from the roof of a building 35.6 $m$ 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 z :s ps:ptn53np+7oir yqx*y d93aki 0i*l3hx from ground level with an initial speed of 60.8 m/s at an angle of l:*p3 xqi an 0:prdiyk*znpyt 73sxos +3ih59 $47.9^{\circ}$ 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- ,l( u2daowkc: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 (k:wou 2a cl,dto finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50jqq 67l37o:2 z ormw3aybiwipnf :o* ,.0 m/s to the West. The plane's speed relative to the groun3 l3oi io,ww*nmf6zqp:r aj:qbo7y2 7d is

  A plane is flying due South w(c j u.y;.qhihjk:2m ($270^{\circ}$) 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 spe9j +hn*liiva +ed of 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 fjo2uj g8f5 bep,al byh*8z30200 m/s horizontally fires a projectile with speed 50.0 m/s in a forward direction 8ubpf j *2,g8oj50behlfz ay3$30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in s nl5 7c hgy0xu2a+/asai 9tfi;till water is 8.0 m/s, is directed across a river with a curre5li0ncf +x2 ui as 7/9hay;agtnt of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 13 m/s in stil v41yww:52i v / h,qhn,mtaghil water wishes to travel directly across a river 0.8 km wide in which the current flon, 1q/:v2hywia tvwi,4hh gm5 ws at 5.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that ca44le 0dmo(7ozqmg-fp n 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 angfo4qoz4ml0 e(- d7gpm le upstream should the driver head the boat?

  A swimmer heading directly acrnj/9ll7 0tr qfcw:xf 0oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstc/7nqx9 fw l0 lftj0:rream 480 m. How fast can she swim in still water?

  A swimmer heading directly across f.c/td.,hn,a v h 2zbha river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is th. h/2 .,vznhbfta,c dhe speed of the current?

  A boat, whose speed in still water is 1.56 m/s, must aim upst;3t vhm uf*sq2*,v36/x (qank wre +hipe(lnnream at an angle of a3;hp /+f* xve, qlhrv(2n*unw nskmi63e (tq$27.2^{\circ}$ (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)  $m/s$