Which one of the following is an example o d/v-;p5g 3myanhir fto,r e;7f a vector quantity?

  Which of the following operations will not changbk +y ws-+r09kz/)iw icfg i+ne a vector?

  Which of the following is an accurate stat vyywc.2sgrtf6 :)cr( ement?

  The resultant of twovrr rwla: -*i5 vectors is the smallest when the angle between them is

  Two displacement vectors have magq kzmb0-dl+f 7 gdveh4l4n-dtg ph( )/nitudes of 5.0 m and 7.0 m, respectively. When these two vectors are addh +04( fln bdt/7g-pe-l4z)mv hqdgkded, the magnitude of the sum

  Two vectors, of magnitudes +pur i 62qf*4mw qpm6i-rtcz :20 and 50, are added. Which one of the following is a possible answpc6r *qq4 p: mw6z2-itui+ rmfer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an g.m* )cyot ai.object in directions that .)i tcmoyga .*are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tcu pvxilf6 +;,he unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's vka:kjdqn2t+ 6 elocity

  A ball is thrown with a velocity of 20 m/wd;b,5f n6 s 9lkccyu.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 resista kex p(xm,r-7(i ojqw 1zijd:7nce, the horizontal component of a projectile's acceleration7p dm ,:z1i(j okxi(- 7jqxwer

  A soccer ball is kicked with a velocity of 25 m/s at an anglltmi* u 2q +pf95hlve:jid+sl vk ))s7a ub*b1e 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 objedq5b(llq7* + ktv eyaa68b*jzct is directed anti-parallel to the velocity vector,*dbl8 jkvbqt6zl5*+ae7y (aq

  If the acceleration of an object is always directed perpendicular to its vu l4c*rfu/l6y elocitru*y l uc64fl/y,

  At what angle should a water-gunj9w h1 .a(zwk(4drirc be aimed in order for the water to land with the greatest9w 4ij(dwrz(kc hr1a . horizontal range?

  An Olympic athlete throws a javelin at four+0uc )m9 wohjrc) 5cjv different angles above the horizontal, each with wuojm95)+v ccjrc0) hthe 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 i(v9fx 9wjjw :/oqt1w7b v;rusecond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would b7j: wjv iwx;obfur( /vw199tqe

  A ball is thrown at an original 0p3cea9v6zur bf l:q1 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 reachz q/h 2wmtk41zboo.;ucd.;rc es its maximum height, how does its speed compare to its initial spbhm;u1q 4.kcod/;toz. 2 cw rzeed?

  A stone is thrown horizontally from the top of a tower at the same instant a gfgo ;v7h yw).ball is dropped vertically. Which object is traveling faster when it hits the level ground below?;o7y .wv hgfg)

  A bullet is fired horizontally, and at the same instant a second bullet a3g g 1m-wcn z7d*xif2is dropped from the same hi7*nfd - 13acg2xg zwmeight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 119.4 m/s and at an elevatc -tn 1f pmt.vvn;gn qm+a2v3*ion of 237 m drops a package. 2.1 seconds later it drops a second package. How fv.nnt *2p nam-m+g3 tfv;cv q1ar apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second laterzk(+ 2ax nj)gm a second package is dropped. Neglecting air resistance, the distance between t2gm )+xjk(nzahe falling packages will

  A pilot drops a bomb from a plx 27i:h;ahv dwi h9.psane flying horizontally at a constant speed. Neglecting air resistance, when the bomb h9viihhd pw a :hs;.x27its the ground the horizontal location of the plane will

  The acceleration of gzbvzv*ru + y2)ap-b ptyg 7:(yravity on the Moon is only one-sixth of that on Earth. If you hitp p)av 2+yyg:vu(*bzt-byz r7 a baseball on the 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 s b5). f.9yyb ws5b8xcptlzn+itraight, level road and pass a car traveling at 45 mi/h. T9. w5 .zs)+ nby85ibpyblftc xhe relative velocity of your car to the other car is

  You are trying to cross a riv:(b ysqe7e8a zrzg--ver that flows due south with a strong current. You start out in your motorboat on the east b: b(vegr- z7ysa8-eqzank 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. How much time 6gk*:pa34 b jter,n ,k .isw*sp8iuvewill it take you to move 12 km downstream, in a river fia,pnpt4ru*sk. j gw:e6v ,ks e3b8i*lowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belo.kb zkrcq5 oq--3mi 8jw the +x axis. The y componq-k5 bjr8 cq mzi-o3k.ent of A is

  If a ball is thrown with a velocity of 25 m/s at an yf7:n;i; dmpg p2jo7pangle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a s0ub *uxfc 4jq9:ggv .l1sgq)0y wg1gxtraight line in a direction north of east and you end up 2.0 km north anduxg0jglysqw:fubv1).14g g0* 9q x cg several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed gfw no 05.)eefof 12.0 m/s. The x component of its velocity is 8.00 m/s.g0oef). 5ne wf The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m lonelqx.r x qzf8ca 8q-e.n78v u:g shadow over a level ground. At what angle is the Sun elevated fe xx7.n8aqr-l8 eq8.uqz v:c above the horizon?

  Two vectors A and B have components (0, 1) and (-1e yd)iu4v lk-3, 3), respectively. What are the components of the sumvui) 3-eyd4 lk of these two vectors?

  Two vectors A and B have components (w15 gkcy9tt ,+t5 xsod0, 1) and (-1, 3), respectively. What is magnitude of the sum oky5 t9tdox5,t +gw1scf these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = ir,8urwe l0 a7A + B . What is the magnitude of C ?e 7a0rrwi,u8l

  A car travels 20 km West, then 20 km South.17voyxo+vy9 e What is the magnitude of its displacement?v 1ye7vyo+ox 9

  Three vectors, expressed in Cartesian coordinates, artgi0qektdbe2 n 80,k*e
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 iode s9p0p /.wzn 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 = (o wh,x )mrim, a+f9hs2+3.0, -8.0), what is the magnitude of vecto owmhf)i, ar hx,+m92sr C = A - B ?

  A runner runs halfway around a circ)k7by qz.k ehzfe.-ca c x +e(me+br46ular path of radius 10 m. What is the displacement of kcqcebe67x-. y) br(+zhz.ke 4 ea+mf the jogger?

  Two forces are acting on an object as shown in Figx j .9rdg/d4houq)s/6o f,b xc. below. What is the magnitude of the resultant forguc/4jd6 sq9d. ohrx )/bof,xce?

  Two forces are acting on an object as shown in Fig. below. What i/b 5lxn1h rgs4s the direction of the resultant h45b s/1rn lxgforce?

  Vector A is 5.6 cm long and poixq6u v(k8;a p j:)ufjonts along the positive x axis. Vector B is 6.1 cm long and pointou puj8xafkv 6(;)q:j s 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 74 cm long and points at v)bw8zel+gf 4 f4vk97li)tc x $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 24 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 19 m/s from the 9hm *8hvyaa5 vedge of a cliff. A stop watch measures the stone's trajectory time from the top of h9h5 m* v8vaaythe cliff to the bottom to be 4.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a brid1qo1cnmp8(kp,a 1 snb gvg*n, ge. It falls 13 m to the water below. How far does the rock travel horizontally before striking thokp1,asq8(b, gn cgvnp n*11m e water?

  A ball thrown horizontally from a point 29 m above the ground, stri3v - +va.osdzrkes the ground after tra 3.aovsdzvr+-veling horizontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an anbut d+pn65 1vg r6w3iyhflzqw1/7;bc6 stv ( egle of 631rplg;heyv zu5tsb+ bfv t16iw (7d q/w6nc$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intoob vlf2 1+gs)rpbil( )y)tuw9 the jump with a speed of 15 m/s at an angle of +lpi(b2 t yfl 1s)uob9vwg)r )$15^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity ofr 0gv ,(hfbjhr *ca8,f 51.1 m/s at an angle of $49.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 26..hua4q 0 u4i ,fvws6ko25wnqn/cadc *5 m/s at an angle of $38.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angt rec-x4ld c49u/ey: yle 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 ho(i 21l njugza; -wur2kf(m,u3xbt3 b prizontally at 24.9 $m/s$ from the roof of a building 59.0 $m$ 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 grouncwuowgwphc74w5i+ c p5(+k/ nd level with an initial speed of 63.4 m/s at an anglehc 7cnkpww(+ 4ocpw i 5/+u5wg of $38.9^{\circ}$ 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 4 ;bt s2lkad6)vjj; bqa 1500-m race at a velocity of 4.0 m/s. If you ranb;jst4a 6qvblj;2 dk) 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 finish would be

  A plane has an air speed of 200 m/s due North, and is in a wine5mgnd )+ i txn(x q8;uk:8xind of 50.0 m/s to the West. The plane's speed relative txixk+ utme)d:i 5; x(ngnn8 8qo the ground is

  A plane is flying dueu *l23u beggz7 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 headzb2ipa5x0jm59vd4w62 bb,(d o e xbaced $30.0^{\circ}$ 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/sz*q0g1 oe0r k(iuynp( horizontally fires a projectile with speed 50.0 mq nzr py1uk*e0i 0g(o(/s 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 i7qxw) /ug rpi m- i.f8(qr)9avoz 8nq6.meva still water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the riv.i8m/q-gq)vi qnae poi) 9xr8 mu (6w7.zrfvaer?

  The driver of a motorboat that can move at 13 m/s in still water wishes to tn5 srd bitl4cg/8j*woin s7: -ravel directly across a river 1.1 km wide in which the currens /ij bds8gnl-57wc:ti4onr * t flows at 6.6 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 wa9nxf1bijm+.jgfjr dz4; * gip1) zhd 2ter wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what anglgfx.f1zij;n j+i 2jd) *bp9md4r1 gzh e upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank v5c0;yf;6udefe0 cz4mvue7g+,xc xhwd w 1t4in 6 mif;y40vxv0, wcte d uc dmcu+ e h6ze7w4f;g5x1n 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rivev78oh(olwia cc: l6t x1)m s2mr 200 m wide reaches the opposite bank in 6 min 40 s. She is swept do cosx2lhw61oav:cimlm( 8t )7 wnstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.11 m/s, must aim upc e;6q79q pu8 rja*tzistream at an angle of e iq ; 7z6tcar9p8*quj$31.8^{\circ}$ (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)  $m/s$