Which one of the follo / a8sv2ojxae2wing is an example of a vector quantity?

  Which of the following operations will not change a vec0zxgdoqf8c 6)tor?

  Which of the following is an accurate statement?ztl,k/ +8o ey *pkh)xgf: lib9

  The resultant of two vectors is the smallest when the angle between t i 6)skb:fd(ggqvdsn*85j ) iphem is

  Two displacement vectors have magnitudes of 5.0w2ofz dz8(n7 s m and 7.0 m, respectively. When these2nz o( 8swzdf7 two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 5rre3ap0ck15gq 3n o.a 0, are added. Which one of the following is a possible answer for the magnitude of ec30ar .5ar3n1gq pok the resultant?

  Three forces, each hav3 w gp6dntf:n2r,nqe) ing a magnitude of 30 N, pull on an object in directions thnt gq3 p:e2ndnwfr, 6)at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unsiugi;o(* nd+,x xcz*known vector is

  Ignoring air resistance, the horizontal component +a6gf*a:)upfh f m rj1of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle oksfcsqbv*0+k6 q p4j)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 horizontal component of a projectile's accele0*pp ki4 /5dobjx.m vuration jpob5/x k u.dip*04vm

  A soccer ball is kicked with a velocityzp c:h40s i-w-a*)q,hmwf xro c+fd. i 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 a2)fgip*,ahm y) xi lm g3+du6qn object is directed anti-parallel to the velocityupmdyhi, ) g2 +3 ma*qf)xil6g vector,

  If the acceleration of an object is always directed perl tz6g6 fe3ykwi-pe* .,b) mrs2f:zsxpendicular to its velocitysfeb:ti l)6. 32k ypr6fm-se*gwz z,x,

  At what angle should a water-gun be aimed in order for the water tcy+(mj3 co6tu4hhe+ no land with the gr(+mj3 +h6otyc hcneu4eatest horizontal range?

  An Olympic athlete throws a javelin at four differe cy9,r .9nrdrent angles above the horizontal, each with the same sc e9ry,r9d.n rpeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. If thefru bof+ ;30wr. whg)vn3k/y o ball leaves your hand with twice the velocity it had on your first throw, its horizontal range ou0.rfy gbnf vr/h+ wo; 3)wk3R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s pco*qx,o (* j1ff/njd 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 maximum height d2bf6g nj(n nuxy(5o,8jmj+l, how does its speed compare to its initiam(n8ldo j xbyn(u,fj 2jg+ n65l speed?

  A stone is thrown horizontally fro8l fwu;typw0y8)g58zmb3 v) vqa3uphm the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level growy 5atmuh v8p3zf)gl);b q38 vywp0 u8und below?

  A bullet is fired horizontally, and at the same instant a second bullet is drt vp:dz b,9nn,opped from the same height. Ignore air resistance. Compare the times of fant p,z ndbv:,9ll of the two bullets.

  A plane flying horizontally at a speed of 68.9 m/s and at an elevavc.iof-19-5ly gfyz c tion of 245 m drops a package. 2.7 seconds later it drops a second package. How far apart will the two packages land on the g.cvc5y fl1fy-g- oz9iround?

  A package of supplies is dropped from a plane, and one second later a second w z5p/ss3 j+lzpackage is dropped. Neglecting air resistance, the distance between the falling packagzs5w3zljs p/+es will

  A pilot drops a bomb from a plane flying horizontally at a constant speeso:w37++sqk dcquu+ cd. Neglecting air resistance, when the bomb hits the ground th7 +od+ksc: q+u3 uscqwe horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth1y/t 2 ix v7jutxoi.q,. If you hit a baseball on the v1yot/u i2 tx7x,qi j.Moon with the 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 axis relative to a straight, level iv pm-tpk*r.+road and pass a car traveling at 45 mi/h.m+ vtr.p*-pi k 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 current. Yd ( r 0vgtbb.:k1i8kgaou start out in yourdtk1gi0rbg(:kba .v 8 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 km/h in s4ei8i0rfz u:yzx9 t;i+4q pq1bv:cpstill water. How much time will it take yoii40p:8 4zqz:ybe9xft1sr vuq;p+ ciu to move 12 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 axis. The 33bt+0y w lbyu6cw0fru01qgc yw f301wclr0 u3ub+t gbq0yyc6 component of A is

  If a ball is thrown with ry r4b4kf cx .96twu6ya 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 ojnx*e1q; 6ig zf east and you end up 2.0 km north and several kilometers east. xgi1n q*;6ejz How many degrees north of east have you walked?

  A butterfly moves with a speed of0 pf5ss rxtzhp;1p30x oj( 8yj 12.0 m/s. The x component of its velocity is 8.00 m/s. Tp;sth 01xj8szojrxp0y3 p 5 f(he angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level g ,o)pklt: xhel*v .z/around. At what angle is the Sun elevated above the hor* :pheakv tlxl o.),z/izon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What f1s*sm*pa d.c are s*p fsd*.a 1cmthe components of the sum of these two vectors?

  Two vectors A and B h)j ru.d iyl-i+ave components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of theseiyiu -j.+ld r) two vectors?

  Vector A = (1, 3). Vect (fxn k5,,qiq 6e9jcrbor B = (3, 0). Vector C = A + B . What is the magnitude 9iqkrn, 5j,fqe6 (xcb of C ?

  A car travels 20 km West, then 20 km Sou2do0w rof7c-r ow xx7*th. What is the magnitude of its displacemen 2 f0odoow7xc7-*rwrx t?

  Three vectors, expressed in Cajc 0yeakr47fjq5 7h /hrtesian 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, expressbxol cv h;kxqq-a(3 -/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) and vector B = (+3.0, oonkorbk z0:ir2;,+(a,m wxa -8.0), what is the magnitude of vector(:o 0r okioz+;b,xk aaw 2nm,r C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is thz.swpx l; .1sde displacement of the joggesxwp lz1sd..;r?

  Two forces are acting on an object as shown in Fig. below. What isafzh(ctw twt q vu8.a1)j//,o the magnitude of the resultant fot/ v1fz.8cu, qwtwjahta) o/(rce?

  Two forces are acting on an object as s8b dz(30hcpb; :tbpsaaah3 3 mhown in Fig. below. What is the direction a pba8bhszca3d3t;0 bh( m3:p of the resultant force?

  Vector A is 3.2 cm long and amnjo0q8f2b s mf 5(*mpoints along the positive x axis. Vector B is 9.2 cm long and poimms2 0f 8*nqo(a5 fmjbnts at $+34^{\circ}$ 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 62 cm long v3b+a8ry 3pmjk(u h 5hand points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 42 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 horizo toduc9c 4jc8 k6w9p7:sp *fbrlr-:fkntally with an initial speed of 15 m/s from the edge of ap7rtfw96lfs8rup oc 9: cc:j-4 k*kdb cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 20 m/s, from a bridge. It8p 40ad qb jsjir;+xc3 falls 27 m 0d;x j +ri8sq3jp4 cbato the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, strikes the grv ./. vd ivmqa*ziys*)ound after traveling horizontally a distance of 22 m. With what speed was it thrdm /vy). **iv zqai.vsown?

  A jumper in the long-jump. q-s x6;lwdip goes into the jump with a speed of 12 m/s at an angle of-q s;di.p6w xl $20^{\circ}$ 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/s at (+hynj p ijvt2 +r 9c;rew:9ocan angle of2 r99+ceyt:;ivjwpco +h(j nr $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launch8 h6fiyzv:q ruox488 oed with an initial velocity of 38.1 m/s at an angle of $29.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initia g:wype90oae +skg9x- l velocity of 43.0 m/s at an angle of $23.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firb c0n6mlr6iq02 rf /to7pji)fed at an angle 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;o4mr (/t8ciealg5dw horizontally at 22.1 $m/s$ from the roof of a building 57.3 $m$ 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 initialr4 64ue,m ,xm +ywtphe speed of 39.0 m/s at an anglhmty+pew4x r m,u6,e 4e 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 a 1500-m race at a velocity of 4.0kt7hj fpm 5 :a dp3.+dhkyhh:- m/s. If you ran the same race on a day when you haddfh:7 5m:3+kt .pjkphh-yhd a 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 s,v)h zkz+gx;ky; waa) , qmo/upeed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. ,au; z,wa)omqx/kg ;yvzk+) h The plane's speed relative to the ground is

  A plane is flying duespe p+q4i*z9h 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/h is 0ikmsm*** -2 b1 ruinj antcx/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 fir5 w se3yjn3dfgb;,gp9es a projectile with speed 50.0 m/s yj 9 pgwe3;bs5d3fng ,in 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 water is 8.0 m/s, is directed across a river witz nnixr*3 kz7/bf28qwh a current of 6.0 m/s. f 38zb2ri wzx7/nk *nqWhat is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 16 m/s in still water:cujqhle ;7.,x6c9 l1dif d.g;kucwt wishes to travel directly across a river 1.3 km wide in which the current flows at 3.5 m/s. How hgw.ljf.1cekt,;;79ludqc uxc6id: long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to tra 8ay* v: sowz nj1 d8d-.6wxfrfnt+pe.6wu m8svel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the 8wf8 odn6jds .- 1s*.x:y ztn8uema+p rfvw6wboat?

  A swimmer heading directly across a river 200 m wide reaches the opposite ba7q 7+;c fam.pc 6abaevnk in 6 min 40 s. She cv qp;cfae67 ab+7.mais swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bt0k.zwv y its8* 8ocid:td*o c.3tmg5ank in 6 min 40 s. She is swept downstream 480 m. What i5cditt. o:t .mdyz *8wks*g0iov c8t3 s the speed of the current?

  A boat, whose speed in still water is 2.14 m/s, morwgws,iokw5bui 6)b9 5x j+: ust aim upstream at an angle ofwk)br:ji ix,6wou5s+ o59 gbw $20.1^{\circ}$ (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)  $m/s$