Which one of the following is an example of a vecto w1:tmgq3pke h6bnkas ,45*xc r quantity?

  Which of the following operations will not c.m .2esz-jxybq.mmm ./ kbq x9hange a vector?

  Which of the followin9 v)b*/ df9vw a4hvkybg is an accurate statement?

  The resultant of two vectors is the y*/s-pk j 8/x3-vvr qjk iubf1)7xy cosmallest when the angle between them is

  Two displacement vectors have molq/syx+ f ;xvm63i 9x 2*gistagnitudes of 5.0 m and 7.0 m, respectively. When these two vectors asy; qt9i 6ix/*mls23 oxvf +gxre added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. t+; ug 2abzkoaib42u9flp( 3m Which one of the following is a possible answer for the magnito9l;tkg42ub u+f(bz m3aa p2 iude of the resultant?

  Three forces, each having g u544ck,pn3rw ) rsfva magnitude of 30 N, pull on an object in directions twfur4p, 5r4nck)3s v ghat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,qnb 0/nlt-m( n the unknown vector is

  Ignoring air resistance, the horizontal component of a projectile'.*vq/r v3qis1n1vv nss velocity

  A ball is thrown with a velocity of 20 m/s at an angle yt5c*joc k) h-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 hor )4,gostsyz r1izontal component of a projectile's accelerationzo gts,syr1)4

  A soccer ball is kicked with a velocity of 25 m/s at an angle u1 ugrx)t 6x5(cuasb9 8 v.todof $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of an objezob s-b(q,hi6 znki 3,xe /o0zct is directed anti-parallel to the velocity vector,xz bk is -q,ien( ,z603oob/hz

  If the acceleration of an object is a+sxnz a)w feub2yrf8as.b6 5) lways directed perpendicular to its velocitsx .ew b abrz52y8)s6funaf)+ y,

  At what angle should a water-gun be aimed in order for the water to l/uke;;y,i 0dyvw 3c doand with the gre y0,;/uki; o e3cvywddatest horizontal range?

  An Olympic athlete throws a javelin (coto45tt9 u ywlku xmu-0 rq84r/x uod:;6khat four different angles above the horizontal, each ohqu/ 98-woxkt546rku:ult 4 0(dyo xtcu;r m with the 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 f5 ,iqaxr 1,o9rwrc*voa9/ d kvor the second time. If the ball leaves your hand with twice the veloci1 /c,ar,w *dkv59voq xoira9 rty it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speedg0* t7 na qpd/:2gempv 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, how does its3gjkx9 hi, xn 03bk4mz zg3kj nx 3 b,9hm04xikspeed compare to its initial speed?

  A stone is thrown horizontally from the toh+z 0pd8mo( 6 hykaof(hgi*x (p of a tower at the same instant a balxhdho0a( zhg8 y (ip(*+fm6okl is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at th-icpe7 r( s1*urn kcs5e same instant a second bullet is dropped from theic rs-7 *p1u(5 kscern same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizonta4hknsj+nua 2m, s8xl1t85 jpglly at a speed of 117.9 m/s and at an elevation of 261 m drops a package. 7.2 seconds later it drops a second package. How far apart will the two packages landnl8km s, 8hu4sj5jp gn+2ax1 t on the ground?

  A package of supplies is dropped from a plane, and one fi-liku1y 3x ;y2tzr5 n9h:n msecond later a second package isk:n-miy9ixz lr;3n5y thuf2 1 dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spmz./;tan 9pgd s v/a q2ee92p iu0wqu8eed. Neglecting air resistance, when the bombg tp/qwe9ae.s;/ m9 u ivuq p20dna82z hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth ofi 0p.h7l+ wbs*5uyrm j 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 Ea.wblrys* i m05+jp7hurth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, levelg odph*co4)l9tnfh ny/0a n 27 road and pass a car traveling at 45 mi/h. The relative velocitocyl/gdt h0* nn2)9 o fnhpa74y of your car to the other car is

  You are trying to cross a river j/e;owhzo( z. that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly we/ (how.z ;eojzst from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take glhy q-:l,ny ,you to move 12h, gn-y:lql,y km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.05w/9*lm l xresf )a *au(qjft1 m at an angle of 30 degrees below the +x axis. The y compo ftjrx(m1*5) q9 f*a ual/ewlsnent of A is

  If a ball is thrown with a velocity of 25 m/s at an an.l, rl3dz 7x; *aldlmngle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in(omi(8liq p*c a straight line in a direction north of east and you end up 2.0 km north and several kilometers eioi(cl*( 8mpq ast. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of is8mzt /da1r vu af5 lq:1,6evmts velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must 6r1f,/zavmetu8la5 d1m:s v qbe

  A 400-m tall tower casts a 6 -od+77tqjs*izu wwq600-m long shadow over a level ground. At what angle is the Sun elevated above the horizonj-sqwotdzq7 i*+uw 76 ?

  Two vectors A and B have components (0, 1) an0x6e-rf, kjvt d (-1, 3), respectively. What are the crj, t-6xevk f0omponents of the sum of these two vectors?

  Two vectors A and B have components (0k5e; ioz hl0 6p*iev,w, 1) and (-1, 3), respectively. What is magnitude5,i 60w epzlov; *iehk of the sum of these two vectors?

  Vector A = (1, 3). teg,4o +wq3jd Vector B = (3, 0). Vector C = A + B . What is the magnitude 3ojqw,e + dgt4of C ?

  A car travels 20 km West, then 20 km So+(ln a*gcwgx.8o4q/ z vu vfvx a)w8-xuth. What is the magnitude of its displacement/+ xl*.4v( 8wvw av ofcuxg-8z)qgna x?

  Three vectors, expressed in Cao)0:2w bpv: dcj h-fitrtesian 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, exprebuww n/6f/2uv ssed 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, -8.0), what is the magnitude oc i::a8,j navxf vector:ivcaa : xjn,8 C = A - B ?

  A runner runs halfway arcx/1 e +t3nsbs5 ym5l w4;cokdound a circular path of radius 10 m. What is the displacement of;s455sklwdbcy +c /ex3o1nt m the jogger?

  Two forces are acting on an object ashtkalj+.v- n. shown in Fig. below. What is the magnitude of the resultajv.lt.+ k-hn ant force?

  Two forces are acting on an object as shown in Fig. belrs7 ikj;46jaoow. What is the direction of the ra r;4 sji6ko7jesultant force?

  Vector A is 3.5 cm long and points along the positive x axis. Vv2za rjo:6i*hector B is 5.3 cm long and points az2:6*o rh vajit $+60^{\circ}$ 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 72 cm long a og,m+ss. t 4n8t6zdqrnd 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 28 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 szgau 7dc hfk8k3r;o +)peed of 25 m/s from the edge of a clif8kc7+do k ;z3)raghfuf. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 13 m/s, frjzk sz z+f1k 270t +dn,nj6aklom a bridge. It falls 25 m to tfzdk+7a1 6s2 n ,+ j0ktznzjklhe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the ground, strikes the grouneu8iw ,)*-3os4)t4x* gqccqnaflos q s*)c4qioo an8tu egqqwl-c*xsf)3 ,4 d after traveling 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 angle 0o2bujk7/xr( jb r.bhof 2ur0ho kbbjxj7 /r .(b$20^{\circ}$ 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 12 m/s at an anglempdeu4 do u9f(*64o ym of f 4(4e opdmdum6o9*uy$29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitdz eyg2t3++ hiy of 28.4 m/s at an angle of $31.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launchedceg*l(*z1aan with an initial velocity of 22.1 m/s at an angle of $35.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angl.vf *jay ;:( .f4kqxobb*xupce 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 horizonta95a+k op9 k*ol:bnzcglly at 26.9 $m/s$ from the roof of a building 38.9 $m$ 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 speed of 57.1 m/s a -33+- raupsax ,xqcklecf,k -t an an ae3lkx+,rfck-3q a-psu,- cxgle of $47.3^{\circ}$ 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),w ro68atlq8.tadx;d6 nm s4t, you can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which 68 n 8o tdqt4wrax,sldm t.;a6slows 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*if7 ak;h *zx.n 4nslv is in a wind of 50.0 m/s to the West. The planek a ;*is*7v.hnl4fxzn 's speed relative to the ground is

  A plane is flying due S 43 jlpb1x2hr-qesj ,mr1aus-outh ($270^{\circ}$) 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 headed1+uy gw* ;c/aavb:ii2h4nb k u $30.0^{\circ}$ 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 3wux 7cgq j0/eb+ x2re200 m/s horizontally fires a projectile with speed 50.0 m/s in ax3x r7w+eucb/ ej 0gq2 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 acr*u18 o(t oukdloss a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the river(* t1uu8okldo?

  The driver of a motorboat that can move at 15 m/s in still water wishes rbu;rw- 86vellwaz,0y 95 l ycto travel directly across a river 1.2 km wide in which thy cavz 06r uy,bwl;-5le9lw8re current flows at 7.6 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 water wishes tox6s;( u; j5z2cpivg4bnzem3gy s t,3b9csk9l travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver he2g; jlzxme; bg3cs69t 3,yvp 5s u9 kc4z(ibsnad the boat?

  A swimmer heading directly across a rvcj-v./wz9h2 p:a qrhiver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can h2.zq-rp c9 v w/vja:hshe swim in still water?

  A swimmer heading directly acruy pw2j 1+q;jndr54gk om98dioss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept do+1 wj q;9ogmpyk 2duin 85r4jdwnstream 480 m. What is the speed of the current?

  A boat, whose speed in still waterx i-y rtk:2/ft is 2.08 m/s, must aim upstream at an angle of :2x/yt-r kfit$27.6^{\circ}$ (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)  $m/s$