Which one of the following is an example of a vector quanti*+qrwep2 fgy(nk 5tu4; 4tbhv ty?

  Which of the following operations will not chanw)bn. vk,ufbx84 g1i yge a vector?

  Which of the following is an accurate w :3uo2 ppxf(hok35ul statement?

  The resultant of two vectors is the smallef5,vpolw pn9 dyc,p(. st when the angle between them is

  Two displacement vectors have magnitud6wb l8:2mvy53pm,twhbu h ugfhg 6v(4es of 5.0 m and 7.0 m, respectively. When these two u48v 3mwh, hbv(fhyg bm62lgt5wup6 :vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which+aw x2ua+rto ( one of the following is a possible answer a a2t(+xruwo+ for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pullbygc4f 2 sv/no lf498,qkr br7 on an object in directions that f94rgyq,4bnk 8b7sc 2/rolfv are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown si 6jk 3mggamn46 ; 4qf11adimvector is

  Ignoring air resistance, the horizontal com +df wex6x671ng(7htxvps +uc;5 tiek ponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s3r:1s3 t cewkv 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 horizonbxk+r8u14 w4 jrjf.0ky- oirk tal component of a projectile's acceleration.uj-4jr+1 of0kyrb4 w kk i8xr

  A soccer ball is kicked with a velocity of 25 m/s at an anas u38d s tg:;sjg+n+ygle 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 directe;7 og7/ef w +ftqswh4cd anti-parallel to the velocity vec47e;hotfw cs q/fw7+ gtor,

  If the acceleration of an object is always directed perpendicular to ittg()jhra1qa x;)gs oa3.-aq g;ar/uc s velocity,x) hoc;arag(r1u.q/aa-; 3ajs) tqgg

  At what angle should a water-gun be a ksnw5 t3e0rn. j.wi*kimed in order for the water to land with the greatest htnj..ks* in035rwk we orizontal range?

  An Olympic athlete throws a javelin at four diff0*jsk g5iy8e9t lkp5x erent angles above the horizontal, each with the 5yje xk8s 5kp*lg9t0i 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 secof)-;dy t ,qcsg*h(x ofnd time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared t*c(df;x-tgqshfy, ) o o your first serve) would be

  A ball is thrown at an/oya7)jip ul.a3(gtn original 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 reaches its maximuo9bw k8 pe*za s94qdz.m height, how does its speed compare 8zzse.kqp 49 ao*w9bdto its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant nr 5rk2ccp h,8eie4hy p)6s9p a ball is dropped vertically. Whipc8crs5h, h4ip n 6y2e)k 9prech object is traveling faster when it hits the level ground below?

  A bullet is fired horizontecx.43/a u rw8ba0i mox wg7g+ally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. e mga.a+8 cxguw4 robi7wx03/ Compare the times of fall of the two bullets.

  A plane flying horizo nzg31-d zmbd9 m:jdt,a2li. 6bd zi.intally at a speed of 84.1 m/s and at an elevation of 219 m drops a package. 6.5 seconds later it drops a second package. How far apart will the two packages land on the g,2a:zdi dbzlm 9zm d6.idb13-ni.jt ground?

  A package of supplies is dropped from a plahdni/74v lh dd2)6 oj +2oviyyne, and one second later a second package is dropped. Neglecting air resistance, the dist vj/iv27)inyh +o 4yhd6 ddol2ance between the falling packages will

  A pilot drops a bomb from a plane fl2 / z 90 e6jvh3yjkdb(p+exaixying horizontally at a constant speed. Neglecting air resistance, whed v x9py0bhejai+e2(zkx 6/3jn 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 v )we-:uj gtr,,hhd :p8-b3z(cxozas on Earth. If you hit a baseball on the Moon with t-zhd u(b:a8c e,3jw:h zxv o)r s-pgt,he same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axisvacl6 3 m)2ku c/oo:ey relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the othoo vla2kcuec 6y )/:m3er car is

  You are trying to cross a river that t)ue(/s 8nhzz 6tj0q vflows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west ba )0 z8tqvjne/sz hu(t6nk directly west from your starting point. You should head your motorboat

  Your motorboat can move atkgbkvo3 *mes 7e +*+txi wgt(. 30 km/h in still water. How much time will it take you to move 1moxg v+. (3ek7ges+ *ib*tktw 2 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axfo oi( fx;2* 8nd0tdyjis. The y component of A ixyjof o( 8*dd2 tf;0nis

  If a ball is thrown witb:/opx-sc 5 vk32fqio + kdl-yh a 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 of east and you end7vb1xh vwv-lf:7hj. z up 2.0 km north and several kilometewj.7hxvz:blf-7vh v 1 rs east. How many degrees north of east have you walked?

  A butterfly moves with a speed(+ lnrf w8b ,5ynw z9ddq*wxr* of 12.0 m/s. The x component of its velocity is 8.00 m/s. The d,bnd q *y5w8rlw(+9 nwfr z*xangle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m lhsih o1 o h0/je0nm*nm3 ktb8,ong shadow over a level ground. At what angle is the Sun elevated above the hoonh38 tnh/01s 0imjk ob hem*,rizon?

  Two vectors A and B have compog20s co to,n0i+7 f rtl0fx9mznents (0, 1) and (-1, 3), respectively. What are the components of the sum ofi 20f0+xromtnsgz9 l0 ,to7c f these two vectors?

  Two vectors A and B5 -nc--yqmgu*a.mpotaz(9 t i have components (0, 1) and (-1, 3), respectively. What is magnitude oazt cp g-5(m*nm-i9t.q y-u aof the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). 2/96cw)nx ,s-rwr vlj kp7odn;j buh0 Vector C = A + B . What is the magnitude of 0sp2nl)k;x/rbw, u9c 7 r 6wd-onvjhjC ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its dx2 , ;nrdiukn)isplackn,x;ui) 2dnr ement?

  Three vectors, expressed in Cartesian coosoi;3tevjb -8 ottu4ulzk n qf)6 (2l3rdinates, 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 Cartesianxpd-la n2 mb c/3wkz,5 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 B = (+3.0, -8.0), what is the magnitude od th06ex:nqq 8qlv )3twc4*ls f vh04)q:nt8tesxc*3l ld6qqwvector C = A - B ?

  A runner runs halfway arz:0eh *ad jk2lound a circular path of radius 10 m. What is the displacement oflhzd02*:jk a e the jogger?

  Two forces are acting on an object as shown in Fig. below. Wh :qkm8o23tac ihtq 1,gat is the magnitude o ,gtci21to :83qqma khf the resultant force?

  Two forces are acting byx726s et+yn7d qi .87fezv0 q;dgmlon an object as shown in Fig. below. What is the direction of the resul;ml2 n6gq8dt d0ez xe7si.y y f7bvq+7tant force?

  Vector A is 3.9 cm long and points along the positive x axiq7c4fn8r6t+ qnddj. vs. Vector B is 8.0 cm long4qnvd6qjd 8 7+tf. rnc and points at $+27^{\circ}$ 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 58 cm long and points anzpeg p k;l,g)/kz1gauko7 .6t $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 41 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 24( 5vxsyt2,dkk m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the k ydt v(5k2,xstop of the cliff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock hor*r8/jfs+bgv 0y i5 tanizontally, with a velocity of 13 m/s, from a bridge. It falls 26 m to the water below. How far does the rock travel horizontally befo y0fsv5ngira 8b+t*j/re striking the water?

  A ball thrown horizontally from a point 29 m above the ground,x u+ wd2sqw-f.3c6mrz strikes the ground after traveling horizontally a distance of 19 m. With w-+df2ucrxqw s 6 3.mwzhat speed was it thrown?

  A jumper in the long-w fx:qiq9.h jlip.kp0 m4sz 3ks/17i sjump goes into the jump with a speed of 12 m/s at an angle of x/ 3is9s iqpsi1 j04 kq7fw.kmz.:phl $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jup uvlu2o+bkhp5;q 0)mmp goes into the jump with a speed of 13 m/s at an angle 5pkol; p)+ quhbm v20uof $26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 51.5 m/s at 7ej+zb0ab *pran angle of $24.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with7d:xv7hbb3y/d jlxw . an initial velocity of 50.4 m/s at an angle of $13.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ,n;pgv96 vyp 1yn kcxo9/qgq4angle 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 hoh u bn-2;vdrx hxs-*;crizontally at 28.0 $m/s$ from the roof of a building 69.4 $m$ 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 fromu )2b6:u cacuv ground level with an initial speed of 51.4 m/s at an )u acv:u6bcu2 angle of $43.6^{\circ}$ 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 vd+59rhcamj8 b zn5+tjuv 36rvelocity 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 ti5v zb8++n9 mraj 63h rtj5vcdume 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 2 cjiwhhd;zv , gr1.ti49/xanof 50.0 m/s to the West. The plane's spehntir vj49 z1/axd wg.h,2i;c ed relative to the ground is

  A plane is flying due /k3;xp sdl;(w sppq-y South ($270^{\circ}$) 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/hvv9m/ew j7cok-nkdg(cf4a d 96rwb ;. 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 firt/o+2mlcy, +tihnh u-ur6 l 2bes a projectile with speed 50.0 m/s in a folhuirbmhln ,t o/c+t -y26u+2rward 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 wa (gqdy.erm(yh8d12( n2fvwdfter is 8.0 m/s, is directed across a river with a current of 6.0 m/s. Whv(dd.emyf2f w(8y gnd2rh(q1 at is the speed of the boat as it crosses the river?

  The driver of a motorboat j1i. uti+t 0ztthat can move at 13 m/s in still water wishes to travel directl01t. tjiut +ziy across a river 1.7 km wide in which the current flows at 6.8 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stulta+;i tl1s- ill water wishes to travel directly across a narrow strait in which the currena tuislt-+; 1lt flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 20vs**b5z zx sg w6)uots(-cc1c 0 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swt5*c) 6s*v gzs u-zw cc1sbox(im in still water?

  A swimmer heading directl- ay6b6c- zmr1 ry;mhay across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed o 66aamc1;yy- zmhrrb- f the current?

  A boat, whose speed in still water is 1.76 m/s, must aim upstb*pstfn-ne uh 3 wnd2eys6/b/i- 8 -niream at an angle ofhw*n yndp/b -6 2fns/iu3itn se-b8-e $23.7^{\circ}$ (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)  $m/s$