Which one of the following is an exampl4y n9 z+1gbr8+le yhxbe of a vector quantity?

  Which of the following operationsrh9 d4b)uf1cs will not change a vector?

  Which of the following is an6hvl:d (gu 4oi+: do y-uc*fsr accurate statement?

  The resultant of two vectors is the smalles*,gt4 xryih4kn a *g:bt when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, re 6d02bcjmjw4 sq:uyx6spectively. When these two vectorx02 :s4qjd6b w6 yujcms are added, the magnitude of the sum

  Two vectors, of magnitudes 20 an*bo x44:fcetx d 50, are added. Which one of the following is a possible answer for the magnitude of the resultan4*xo f xe4bt:ct?

  Three forces, each having a magnitude of 30 N, pull on r g-a r/gls;8i,ql;py an object in directions t-girs,/8y gl a;q;plrhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the u2rrry ;g 1djecu; gds36m m+n*nknown vector is

  Ignoring air resistance, the horizol0/9v u .j2kpslp6u 5zyx3yw zntal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at ane1. vm rg1n *ejnmwyj.*kpb.7 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 projectilh4z gp2w+/tijh cz ll8w2*v*we's acceleration 2tp lhwz2 ihj*+/84cwzlwg* v

  A soccer ball is kicked with a velo0 cfi2u 22itfzcity 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 anti-parallel tov;l0pk3*;0bh bu xy nld wkl5: the velocity vec b5*xkkd;uv 3n :0llp b;lh0wytor,

  If the acceleration of an object is at ejstf7dvj02a99*aowh-yf: lways directed perpendicular to its velocity9jf2fj7a:9tt*o ahw - esy 0vd,

  At what angle should nmf,sh /.tvh9o ;wl:j rhmit5445 xeea water-gun be aimed in order for the water to land with the greatest hrmn4 mxoh,e;il/t.t hv95 :5w4ehjs forizontal range?

  An Olympic athlete throws a javelin at four different angles abov nmu45;dyy1kie the horizontal, each with th1my ;k 5uny4die 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. If the ball leavpq rh)(l g:pqn0;5d kees your hand with twice the velocity it had on your first throw, its horizontal range R (comqe lpr0;pd(k h)n5g:qpared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at x d4x7bwvuxvs1h y+-4an 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 r :ikfsj.5hc 7e2x2 cdmjz(* fleaches its maximum height, how does its speed c.xkcms5: 2d *flj2 h(f zijc7eompare to its initial speed?

  A stone is thrown horizofw5 uq 804fokdntally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faste q0f854kwdfuor when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a secone92ney vj z r6)rtmb3/zl, (eqd bullet is dropped from the same height.,z3r e( j)9zeqb2l6 /nvt myre Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 6r-x53y pcmn*6 culu 8msp3xq20.8 m/s and at an elevation of 205 m drops a package. 7.6 seconds later it 3qm 6xp85lmuc ryxns2u*-3 pcdrops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, an;udd bc+:w5,9. i3pte tmgxzdd one second later a second package is dropped. Neglecting air resistance, t t:9 , 3gdd;cbp.eix+u5mtzwd he distance between the falling packages will

  A pilot drops a bomb from a plane flying horizo+7 0geuz ;yomxntally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal o+ uyg;0me z7xlocation of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth--z+7d7 m9u 2oqfjzasgny(7ot bwy;t6( vmsw. 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 would 7f;( bd7vwo-z utaz -ygost +7ynw9s m( q2m6jland

  You are traveling at 55 mi/h in the +x axis relatvj0 l-bp1cp i6ive to a straight, level road andlvijp1c0-6 pb pass 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. Yoymt 5l. rmx7;lu start out in your motorbmy;mt xl.57 lroat 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 still water. H2 agr0pn 7(d 4tv0 (wnf*wa/vnm z2bzlow much time will it take you to move 12 km downstream, in a rifz 72na( v4plmt/rw*g2ab nvd 0(n0zwver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degreee35n, 5pfc 6jwzdcki:4 *q wyps below the +x axis. The y compok,eiww64 :py 5cnzjqf c3*pd5 nent of A is

  If a ball is thrown with a velocity of 25 :y o 9.i i5yrlqdud*2pm/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 dire3 ,qfvtxetk ; eb) sr56h(g8pection north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you walked?)fe b(6p,;xtrg5khee s tv8 q3

  A butterfly moves with a speed of 12.0 m/s. The x component of itsuyq1+n a)c9eyy 7j6hzx-o ;nk velocity is 8.00 m/s.k)q6zcjx yo;y9-ynu7a eh 1+n The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-iywrv p ; ;3ka)riq( 4:p)odrt4sa,hfm long shadow over a level ground. At what angle is the Sun elevated above the horqi4p ta4rh);r): o frp;k ,avi(s3wydizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respecti).tzj+d k pt*vvely. What are the components of the sum of these twpdkt.* jvt )+zo vectors?

  Two vectors A and B have componentc w3(nfrug brd*9* .iys (0, 1) and (-1, 3), respectively. What is magnitude of thedg9 .c3u (*rnrbf y*wi sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . ttap7c:yvm ) ( What is the magnitudact(m typ7v :)e of C ?

  A car travels 20 km West, then 20 km South. Whatmsfl ;ae30pb: is the magnitude of its displacemfsalb: ;epm0 3ent?

  Three vectors, expressed in Cartesipew7h, ny8(o eyq/g-rmg -r ;21 mamhoan 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 coorkpuk r4aqes k8 39iy-+dinates, 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 magnis/ e1-, whs+mpv8uej dcp,+fitude of ve f+/s ,es 1w pjmuhc,pd-8i+vector C = A - B ?

  A runner runs halfway around a circular path o36xy )yweo6wu f radius 10 m. What is the displacemen)uo 3xwwyy6 6et of the jogger?

  Two forces are acting l+g c:zefe.f no7ah)s; 5ix,mon an object as shown in Fig. below. What is the magnitudeo7m:5ga f)c zne,.i hxe +fls; of the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is 5xq8 us6el4jq the direction qseujql x45 86of the resultant force?

  Vector A is 5.5 cm long and points along the posittac 6 b*xrp php7er (y9;g58owive x axis. Vector B is 8.2 cm long and px 6e;t(bpa yg9 8or*wrc5pp7h oints at $+50^{\circ}$ 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 70 cm lo6vqn9o05 c oug3e)t ppng and points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 50 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 21 mk 2i. fe-2s+3p(rvav g nxxq0m/s from the edge of a cliff. A stop watch measures the stone's traject aigxnxv r.2+keq0pv3( mfs-2ory time from the top of the cliff to the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 8 m/s, from a bridge. xsf9:slyr t0af/4 8 piIt falls 13 mpfs s8r 9/:fai0lt x4y to 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)d onz/k;mg3j ;:igpf the ground after t;g:f3m o/ p; zkijdng)raveling horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s hv u0raia,ux2t ,a l20at an angle ovlth2 2ur ,0xaa0 uai,f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes i7ni-+ s9i jyo.h8wdrc7uqd . s ;jb6ointo the jump with a speed of 9 m/s at an angle ofsi8; 9.suioi.ojrc y hwq7 b+j 6dd7n- $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an init x0/51uuqlwzsi 9n1q1xklo8hial velocity of 55.9 m/s at an angle of $27.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity udc/-ev t ca-bw3s8b.l img 6k980ygtof 24.8 m/s at an angle of $23.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fire r6utgf lv*4e3-8vvcc d 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 horizontally at lnh 7b)d-g0j6un2iu;o art rgyd(+ 3o21.9 $m/s$ from the roof of a building 63.8 $m$ 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 initial speaa2p;/m:quj(+mv aumed of 66.6 m/s at an ang2(:pa m +/auv;m mqajule of $38.0^{\circ}$ 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 : wn/uw+c d(urvelocity 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 u(wcw /dn: u+rtake you to finish would be

  A plane has an air speed of 200 m/s due Nortd(cm nc+8ed ,t)y1t b.ty: xvfh, and is in a wind of 50.0 m/s to the West. Thef 1:nt ybc8m )+,eddx t.vtc(y plane's speed relative to the ground is

  A plane is flying duecovtm4c2+6upup -go( 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 (m3/ 9mxjkb6b5 1qihwuo qc;h120 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 deonff7 q;g64horizontally fires a projectile with speed 50.0 m/s 4;e 6fdgof nq7in 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 direc-yxeyx.) w)h8n951hb vvwr ujted across a river with a n ) eux195v)hxwywy-jb .hr8v current 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 16 m/s in still wvu ,2h0ihpc/h ater wishes to traveliu/0h2hv ph,c directly across a river 0.7 km wide in which the current flows at 4.4 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 water wishes to trave)v*ug/qzs 680 imsi ail directly across a narrow strait in which the current flows at 5.0 m/s. sa z m)6gvs 0iqiu*8i/ At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 mt;( cylhix9tzvyb.i .) (wk3q wide reaches the opposite bank in 6 min 40 c twbty( kql y;3x)v iz.(h.9is. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wid1ff :i (z/4ff ual*mdie reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the curr:ai4uff dzf *1mif l(/ent?

  A boat, whose speed in stilld7 pr+s6uo n/z water is 1.73 m/s, must aim upstream at an angle of n+r7ou6 dz/ps$23.3^{\circ}$ (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)  $m/s$