Which one of the following is an example of a vector o zmjkgzi/gl54e 2n9.quantity?

  Which of the following operations will not change a vect)dk pc. q(a-seor?

  Which of the following is l1 b.*xf 9mgyran accurate statement?

  The resultant of two vectors is the smalle4y/* nsv h6vw j04vvle*v m sl26lf3gqst when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectitpd(w4p2ec8dxep td8)zs6m 6 vely. When these two vectors are dze 8)ts26t4 p(epdc8xm6dw p added, the magnitude of the sum

  Two vectors, of magnitudes 20 andzp-k 9as 90l.qvdh6gk u+wmgh ;y,r, f 50, are added. Which one of the following is a possi kmhpy6r-fk d,s;u wal+v9g9,hg0zq. ble answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an obje9-jj *enr*gi1en af gj wb .li//yit8+ct in directions thaf9ei/b *jta/i+lg*.n rjnj - yg 1w8iet are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectowwg +hfb qs3 yw)/dr8(r is

  Ignoring air resistance, the horizontal component of a projectile's velocite 9n,dl8tzc :*y+dhwty

  A ball is thrown with3,s xmltk (9bh 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 horizon* er 5991a uztafkkiu2z0ny r*tal component of a projectile's acceleration t9aika* r0z9rzf2e5n 1u*yku

  A soccer ball is kickun/ b,a wwx3bu,yvn(z r5z0k; 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 direc3s/8oa aw1xeshj2 3l ijlol0(ted anti-parallel to the velocity vector, sso8jl0h iala3/ ejw3x o2l(1

  If the acceleration olkhgu o(8,sn) -.ccqa yaxy s5h+(rk o.iz-)qf an object is always directed perpendicular to its velocit hncy8ri. +- y xhk-soqlazao,q)s .5(gukc()y,

  At what angle should a water-gun be aimezi(5/wo7fk -u x )9vrnz x3mncd in order for the water to land with the greatest horfxnk7z ovn-u5x rm3wz /(9 )ciizontal range?

  An Olympic athlete throws a javelin at four different9dhx 0gmxkf-3 angles above the horizontal, each with the same speed: d0fkmx39g-xh $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 the ball leaves your hand w3auy9u /8tqcg5dk6k yith twice the velocity it had on your first throw, its horizontal range R (compared to your fidqkc8/u3gky 6y5t au9rst serve) would be

  A ball is thrown at an original sp .x6 jw0jei-8/yusxnpeed 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 maximum height,mk1; j4mrx d.s58lu 2nl6a dpz how does its speed compare m a5jlus.p 42zrld;6 kd8mx1nto its initial speed?

  A stone is thrown horizontally frofg ;0xo hogm81m the top of a tower at the same instant a ball is dropped vertically. Which objecto mg0f8;go1hx is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second g0 lfyifwe: brg3q/fg6+zt7cm/uu 7-bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of76iug r qy0gfetf+zc 7b-lu/:3fwmg/ the two bullets.

  A plane flying horizontally at a speed of 54.3 m/s and at an ez kd t;*rdh,j ; *-kvw,tlwg: 6x7gulclevation of 295 m drops a package. 5.9 seconds later it drops a second package. How far apart will the tw ;rwttc,dkl:kgz *6x7l-whd; ugj*v, o packages land on the ground?

  A package of supplies is dropped from a plane, and one second later 93r ).5gxuvqqdkv)qc a second package is dropped. Neglecting air resistance, the distance between the falling d v)9g) uq3vrq5kxc.qpackages will

  A pilot drops a bomb from a plane flying/jm (+ c:0gofmw-t, po wptcw- horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the octw w p t/p0,mgj-o:(f-mcw+horizontal location of the plane will

  The acceleration of gravity on the Moopws*;z lbiz6o4zw1m6 f tk8 z4n is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the b4so ;wizw 6m8zl41kf*tbz6 p zall would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road arn)mqf p0d*mq; oswm c,v* jf18 t5(bwnd pass5pnf1sb,fm**q wqm c j(dwvr t0o )8;m 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 th1f ll8yz0 rystc;92ej at flows due south with a strong current. You start out in your motorboat on the east bank desiri9fz1y;t2lec yjl8s0 r ng to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move i im7nobr6) *t b6 vmoht0ie:(at 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river f o m b0bev6)m(i*h:oi i7tn6trlowing at 6.0 km/h?

  Vector A has magnitude 8.0 )rasz cn5euxa(5f;o,m at an angle of 30 degrees below the +x axis. The y fa)a, nxcer5 su5oz;( component of A is

  If a ball is thrown with a 8:s kodg2j 8v fy0ak 4fi(.djh2xe5ukvelocity 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 stra arn4-i g f1lj+,o7ebj7+cfgiight line in a direction north of east and you end up 2.0 km north and several kilometncffj+i7gbr1i 4l-o j +7,ageers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its ve mh(-bah.k*jy0.nq uslocity is 8.00 m/s. The angle between the direction of its motion h q-.m jyak.b(*h0nsuand the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a levsnk * oo5 m 0llvnig/8q-cbwn7u0/b(yel ground. At what angle is the Sun elevate* y7unbng c8l/ 0kqoms0 -wv/lo5n (bid above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respeh 1c0+.kwk rfcx.j +yfctively. What are the components of th.c ff.k1+hyrc+ w0x kje sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What //m0 266cdtnrcmeihc is magnitude c2rtem60cnc h6/i dm/of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vectoqx9upacwkoj1+8 un 4jg5fnf ;6/x- vdr C = A + B . What is the magnitude of vu q46-gk+jn 9 puad;njwox ff58x1/cC ?

  A car travels 20 km West, then 20 km South. What is thenz+,h ;noh)e- rum g,e 42uria magnitude of its displacemizr,a n;m -,nh24 o e+uegruh)ent?

  Three vectors, expressed in Cartesian coordina )(o)uf6p7 zpi bh-;kuzto6o od 4bs(ates, 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 coordinates, a5r -qpw(q)x hyre
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), wha6b e/6ge5ct,c fl9c gkt is the magnitude of vectc5e/k ,c9t egg6l fcb6or C = A - B ?

  A runner runs halfwayu:n a :i(4ybfs*lg*hz -sd6iv around a circular path of radius 10 m. What is the displacement of the jogge:ns i (zhv4:bl g6uf d-asy*i*r?

  Two forces are acting on an object as shown in Fig. below. What i/ q(ugpm. ) itd/ejv:es the magnitude of the reitj.d(pm:v/e ) gq/uesultant force?

  Two forces are acting on an object as sz ubi ;p(y(;hbhown in Fig. below. What is the direction of the resbb yzhup;i; ((ultant force?

  Vector A is 4.8 cm long and points along the positivebag4s+ , xcjdh8qkj4, x axis. Vector B is 7.7 cm long ajdb k8+ja4 4qhscxg,,nd points at $+48^{\circ}$ 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 61 cm long and poi)qdo (jist t1)nts at $30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 27 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 rle:,.,o;4 s sf ye5iabsa1iyntally with an initial speed of 25 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.3 s. What is the height of the clify,a,yl15si:4b ;se oaes r.iff?

  A girl throws a rock horizontally, w9,q9ioye msmpk3h .i13x7f vn ith a velocity of 18 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before strikiniqo.pe vki,3y97m 19nh f3mxsg the water?

  A ball thrown horizontally from a point 25 m above the ground, strikes th*-f x+3)v/dse jk ygise ground after traveling horizontally a distance of 16 m. With what speed was 3/dj i*yse) vxgkf -+sit thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 c ov nkzw.)6f9m/s at an angle o k)z fcv9o.w6nf $20^{\circ}$ 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 1y2x90c+(o; xpsxjbc5qg5 oz q5 m/s at an angle of x 2o5c9o0 xqzgs(y+qjc5p ;xb $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 54.7 mktgvn d6c:6w hjqev dl/ )i7*5/s at an angle of $10.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launcy3zm,tg6xwxr* a /j 1ihed with an initial velocity of 52.2 m/s at an angle of $12.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglz j- m29gtnua)e 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 h6i5 b ogr+ba7*a d2.u j(ats/hgf/z usorizontally at 24.4 $m/s$ from the roof of a building 57.4 $m$ 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 from g3uu)eub yf z;.c8n0iq round level with an initial speed of 37.0 m/s at an angle ofe).3cb0z8 i;f qnuyuu $47.3^{\circ}$ 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 d 0 aee(g/rhf-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 to fif/hdgae( 0e -rnish would be

  A plane has an air speed of 200 m/s due North, and is in a winpa3al// 4 0hkvq 8erz9ktu-zh d of 50.0 m/s to the West. The plane's speed relative to the ground isqv/8l4kp h-e/9khzra 3 u0zat

  A plane is flying due South wivm6ng26 z5nj (2o6s.se8oe du*c mz($270^{\circ}$) 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 12a. 3k8tf di6xadx 1hr(y +mz1c0 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 projectile with sp.( njjse)xt0 em,y-meg wyj9;eed 50.0 m/s in a forward diremej(t0,-.y; s)nmgy9wxe je jction $30.0^{\circ}$ 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 di(xyl6f o2 m1xtrected across a river with a current of 6.0 m/s. What is the speed of the boat as it crossesy(fxxl1m t o26 the river?

  The driver of a motorboat that can move at 15 m/s wl2vfjrk 147(6ovjzhin still water wishes to travel directly across a river 1.9 2(h6j1 v vlrz7fo4wjkkm wide in which the current flows at 3.2 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still *z hx;;mxk* c, u.rhz2bc gx9wwater wishes to travel directly across a narrow strait x;zxrbhg,*.wx*hz 9k cu2cm ;in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading ditsne bbso82iqf** : m/rectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim b*s*bmsi:q 82tefo n/in still water?

  A swimmer heading directly ac;t.cdw78 a5q hkgnv xr3tq 6mil;cw9+ ross a river 200 m wide reaches the opposite bank in 6 min 4;r 8+nl9 6.t5mc h t;dq3wxqa 7iwvcgk0 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.83 m/39a rkeu 2-ex 6aunpmx4yu( 9os, must aim upstream at an angle ofeax439-m 2yp (k 6xuu9aueorn $22.1^{\circ}$ (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)  $m/s$