Which one of the following is an example of a vector;)1* vyyt u/czmh0akx quantity?

  Which of the followin c,0fa, dm+but2 w: ok udi.z/ab/xq.kg operations will not change a vector?

  Which of the following is an accur wt .4ve* g2j co3ao3ncwpn7+8veerh5 ate statement?

  The resultant of two vectors is the smakblr5 hg7blhm +.cn 97llest when the angle between them is

  Two displacement vectors have magn)rvl8shn(lsl 4jp -.ht-yi4 a itudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitaljirs 8-hh4-4vp l )ln.s(ytude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the f .qu6j5 ,yjzjfollowing is a possible answer for the magnitude of the resultant?,zy.j 6u5jj fq

  Three forces, each having a magnitude of 30 N, pull on an object in(z:ga o c6kct+ directions that are ogta(zc6c+k: $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown viejd5ue -w i c.e; )nbn96 v qu)6g6-iu(xujfxector is

  Ignoring air resistance, the horizontal component of a projectile's velocin( .yazeg u,1fty

  A ball is thrown with a velocity of 20 m/s at an anglp 0n :+w53 czy5 rq;yrsw6xgsoe 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 ;1oj0pzj4,pg7* tmmg/xkni h a projectile's acceleration,nx0h/jp*jo;k mg4 z71t pmgi

  A soccer ball is kicked with a velo wcen284+i enecity 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 an4( k+b gtlxlg-ti-parallel to the velocity veg+ x-t4lkgl( bctor,

  If the acceleration of an object is always directed perpendicular to i6x1rk3w txbq a,fh yjb8,6-sf ts velocity,-1t8b3jh x6 rs af,fby kq,6xw

  At what angle should a water-gun be aimed in or, s0klr9sz4csr y9m32g1eul bder for the water to land with the greatest horizonu4 cbr lek1rm y,99zs lsg023stal range?

  An Olympic athlete throws arw -y+kz .x4:-8.pqo q ugfzfb javelin at four different angles above the horizontal, each with the-b+k4.rxpf.oyqzg:uw- qzf 8 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 second time. p+8rw vtxrzv cx)r+3 * If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R x+v+v 8*wc rt3zx)r rp(compared to your first serve) would be

  A ball is thrown at an original speed of 8 gq oxg6x )qm1phup,u77/p-ki.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 a1 kf 17+bkg: zyys0oqyttempt reaches its maximum height, how does its speed compare to its initial speeo y ys1yk :0kzbfq+g71d?

  A stone is thrown horizontally from the bkpn+35e 5ostq(a0sb w2 /ttrtop of a tower at the same instant a ball is dropped vertically. Which object is traveling far25 03/ow(tks5st tpqn b a+bester when it hits the level ground below?

  A bullet is fired horizontally, and at the same in 01(:al1cbpi,+pw kr 4sy1pw d kyscg3stant a second bullet is dropped from the same height. w3 idw1 y4y kp:sp,s1ap+cc l1kg0br( Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 110.3 m/s and at an elevati3 )sb4fbzuvd0+k * qe e8ldj8yon of 262 m drops a package. 2.8 seconds later it drops a secj+buqk 8yfesb80 vd 43de)z*lond package. How far apart will the two packages land on the ground?

  A package of supplies ix 4aj,v,ps*i ks dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance be, sx,p vj*4iaktween the falling packages will

  A pilot drops a bomb fromp+ 1gk 2akaqb4a 7;dug a plane flying horizontally at a constant speed. Neglecting air a;g724g apbdaku+1 qkresistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on toen;:hsn:i2p os1 9em he Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at t:e29sinh n ;po1moe: she 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 r (rx ijqu:tg/)oad and passqt):xjr(i/ gu a car traveling at 45 mi/h. 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. Yo3z hs 1 mo g:kw5m5fw9p:0ivbyu start out in your motorboat on the east bank desiring to rea50i:b 9:kvyf pm og5mswz31 whch the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How uqh,g 9i0,ajsmuch time will it take you to move 12 km downstream, in a rivei,sua 0,9hqjg r flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrea+8mgf vq9c:kqw6az 9es below the +x axis. The y component of A kma fw9q6ca9:8+ gzvq is

  If a ball is thrown with ajc;:mxk;.-kq;3 l:xql4,k qm x 2xuuxoagjz. 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 mr sj /qh0)ou4and you end up 2.0 km north and several kilometers east. How many degrees mo)jq/ 0u4hrsnorth of east have you walked?

  A butterfly moves with a speed of 12.02r jkhb2mmbv/cj 0*dz)oh f89 m/s. The x component of its velocity is 8.00 m/s. The angle between the dir f v/*cmmdbh8o2)r j kzj92bh0ection of its motion and the x axis must be

  A 400-m tall tower cas0u qvrmenciw.e l/n ,tc, p164ts a 600-m long shadow over a level ground. At what angle is the Sun elevate,0cnmew/ .6 l1rnequpv ,t4 icd above the horizon?

  Two vectors A and B have components vjr kpk))v(4a(0, 1) and (-1, 3), respectively. What are the component)vr k)kpv4aj( s of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiveldyjn1;pgd zful b q28an*e 40sfi)8t( y. What is magnitude of the sum i)l0e*g sp fqj t1ndzn d4abu;2y( 88fof these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = i. cr; cnvg/xji)qy5-A + B . What is the magnitude of C yr cxig5vc) i /j;-n.q?

  A car travels 20 km West, then 20 km South. What is 5 )mdfdw*fy/pl))u v liy 4j6uthe magnitude of its displace)dl)l/6vy) fyidfm p5wu*4ujment?

  Three vectors, expressed in Carteh6cv q7e5l ,pu6.rptesian 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 coordemte f x;;7t0u*cqj, 80 rafwrnta;)hinates, 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 magnit fqs.l .sqh/3tude of vector C qfq ..s3l tsh/= A - B ?

  A runner runs halfway around a circular path of -pmg1ryl); 3iur0t 39yqqnviradius 10 m. What is the displacement of; i) q-ny10tm9p3yv gr3ui qlr the jogger?

  Two forces are acting on an object as zeydbv /iu/3 0y+h1 rgshown in Fig. below. What is the magnitude 3/ydy1ug0bvezhi/ r+ of the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the dire:9p(hk lmp vquwa 2wf3k0pz((ction of the resultant lpmu(v0 afkkw23:zqp 9h( (wp force?

  Vector A is 4.2 cm long and points along thepqm9s)80slzxs0 hf b3ac b):h positive x axis. Vector B is 8.6 cm long and points at89msb p3h fcls )sa:)0qbx0hz $+59^{\circ}$ 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 51 cm long and points )6trd u4p9 qa+inqui 3at $30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 39 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 17 xnxemcd 47)r2h(pa/ y*uqaz p2w-m+hm/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to-apx e w /nq x4y(czh2)7pm*umdr2+ah the bottom to be 2.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bridge. Itc n)td )66 exfbdgc i,u-/vjp6 falls 16 m to the water bel jng,vibdpuf)e/ dc 6t6-cx6)ow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the dz:: q enaxqayi7k/ 0+4i2cihground, strikes the ground after traveling horizontally a distance of 16 m. With what qi:0dq2 7 ha:n kxy ia/e4z+icspeed was it thrown?

  A jumper in the long-jump goew)kab d)2 -wwjs into the jump with a speed of 12 m/s at an angle j2wb) k)-dwwa of $20^{\circ}$ 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 juwhrtb -, +o*6mq3p+hkdqi8k mmp with a speed of 14 m/s at an angle +phqq 8owr- 3m,kikm +bd6t*h of $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity ofs s/trn50r(j z 23.2 m/s at an angle of $27.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 51.1 m/s at an angleu 5mmxmim4t-9 flzprzp8/ j*) of $46.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an o7:z c)opw-ba:nu ee2angle 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 hornkw jm*ew1.jt3c1bb c0u*k/ wizontally at 25.9 $m/s$ from the roof of a building 51.7 $m$ 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 wiqvl u7+5y dhozeev 9-9th an initial speed of 39.3 m/s at an angle795 ud +vz-qhelo9yve of $47.9^{\circ}$ 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-m race at s,z.hfl n6zy0lxzwvv6qj3 85a 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 would0. vxzn65 w83vls qfy,zhjl6z take you to finish would be

  A plane has an air speed of 200 m/s yvv8 l9aecuad6(2wtf7bj),d due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground is w,(v6al7tf2cj8d vuae)bd9y

  A plane is flying due Souyrd zb(t:x w+xc 2xo)0th ($270^{\circ}$) 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 spe+3 bdlbttchvc; kk33:a l9 4kxed 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 200 m/s horizontally fires8 l r( r+oma487ixbqpc a projectile with speed 50.0 m/s in a forward directl 7mp io8b+q8cr x4a(rion $30.0^{\circ}$ 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 withvnw oz u3)5/ko n/s.te5s9e pi a curr 3z.wnso/s ote 9kvpe/5n5u) ient 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 19 m/s in still water wishsk v .xcpua-gi1)ks-/b, (s mtes to travel directly across a river 1.8 km wide in which the current flows at 7.0 m/s. Hos x. /km(pb k- i1)vtga,suc-sw long will it take to cross the river?

  The driver of a motorboat that can move avaem +ib52y9p 5 tylo .xd0ou9t 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 angle upst+. opatemb0vo 5x u 9iyl295ydream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reache)arfql q do0 6(nf*pd/s the opposite bank in 6 min 40 s. She is swept dofqo0rd )*6 aflpq( n/dwnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m ek9.n(pyvw), 5p vgte wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. w. y,gk vetne pv95p()What is the speed of the current?

  A boat, whose speed in still water is 1.22 m/s, must aim upstream at av q8.mak sd73vn4/dyzn angle ofsnda/mvv z48 dk3.q7y $27.5^{\circ}$ (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)  $m/s$