Which one of the following is an example ofll; 4jgu7x9l d a vector quantity?

  Which of the following operations wimb qr 7i)7 :5j vikp dxcdxl9hz,qj,87ll not change a vector?

  Which of the following is an accu8zk-sg (es7fw /kd9q:k*0lpzqz udt7 rate statement?

  The resultant of two vectors is the smallest when the;e1 /3wdxlc 4.pug ij.yxwk )q angle between them is

  Two displacement vectors have magnitudes of 5me0mgq- ms u /fz84igu0q nf54.0 m and 7.0 m, respectively. When these two vector0-qmu n08q/fs5mgumg eiz44 f s are added, the magnitude of the sum

  Two vectors, of magnp)hfolg 5sx0-q+v 6 t2fam/if itudes 20 and 50, are added. Which one of the following is ai-o)6tavfp 5+mxf hf0 qs/g2 l possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pulrqmh+/3y :qk.bf5 n2-kdc zhxl on an object in directions that nm c kqxkh52z/r:-qhbyf.d3+are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknow ib6ivhpr1 *6xn vector is

  Ignoring air resistance, the horizontal comp9pu ;g(fqwq - h(jha5zonent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s atwkg4pd3tuegy y:*h9/ xnr d /;ixj: l( 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 horizontal component of a projectile diuwuh/ a4c0;'s acceleration/hiaw uc4 d0u;

  A soccer ball is kicked with a velocity of 25 m/s at an*s 0mzv4d3dos 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 an. o)ym..wl fi7(qavsd ti-parallel to the velocity vls..aymvwd i.7) oq (fector,

  If the acceleration of an object is always directed perpendicular to its velock8gqzt.x )6r1eu ipl om,u:g 1itye 1m.l6o:) ,zur 1pt8ik guxgq,

  At what angle should a water-gun be aimed in order for the wanis.( ,i71cpqv*qsj zter to land with the greatest horizoivc(,nqjszqsp 7. 1i *ntal range?

  An Olympic athlete throws a javelin at four different angles above the hordc, 8nsoyr2amo ev ,jd ;3j(v3izontal, each with the soecn3v vd (d2 s,rya3m;8jj,oame 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 td t(d0re0a *vup,y n:lime. 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 0: *ydp0te(d vu,rnalbe

  A ball is thrown at an original speed of 8.0 m/s at an czeh+r,d +4j)kh vz+eangle 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, hip-c7na2 n yeo46x l3dow does its speed complaoxp-7ceyi 6n423 dn are to its initial speed?

  A stone is thrown horizontally from the topr-t lrlq ; 9r k qs:,:6i0si3eycc)slh of a tower at the same instant a ball is droppe3)i :i6r yq;h:c,k0e srcll ltrs9- qsd vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a*-duto 3j.rw5oxud6 p9ib) eb second bullet is dropped from the same ut o.ji prd 5bode3-b9*u)6xwheight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 97.2 m/s and at an elevation or zeclo2v: ax2nb.v 0ko+a5n)f 148 m drops a package. 3.3 seconds later it d0r 2v oknx+.z5b:2v o) clnaaerops a second package. How far apart will the two packages land on the ground?

  A package of supplies is droppez7d2/itl12ojk)ynau s+ k l/k5vy shgiu6g61 d from a plane, and one second later a second package is dropped. dgkz6k22 7tky+g 6jahli) siuv/o11 nslu /y5 Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane f*kuch .v;tq-q l5i/gh lying horizontally at a constant speed. Negleh */gqt.culqh -k5i v;cting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth ozaa.o( y )(fcmhd(san4n ,j)ef that on Earth. If you hit a basz(a dao(ey(n ).) j,4fmah ncseball 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 ckk+2m.0 feopy inr+)straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car tn+ k km ref)p0i2cyo.+o the other car is

  You are trying to cross a river that flows due south with a strong currevy xqkx/;: t4l p. 37kws6sfognt. You start out in your motorboat on the east bank desiring to reach the west bank directly west frox;skl.6x p/kft 37ygow s4vq: m your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still0uby vdf0l,; v water. How much time will it take you to move 12 km u0vly ,0dvfb; downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degreesqx w.plk5n0v x4b.g a3 below the +x axis. The y comql. v3 xg5nwp4 ka.bx0ponent of A is

  If a ball is thrown with a velocity of 25 m/s at an anglc t9c( p2n5mtwe of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a stym/zynws;0 0i qd x,c+ ;hm5ubraight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you wdsuy/ qmn yhizxw ;,m+b;500calked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its xys51x*hvs 4lvelocity is 8.00 m/s. The angle between the direction of its motion and the x axis must b4hx yx s*ls15ve

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what *rvs5t/:wi ,qe0cp b;og0r mfangle is the Swvq5er0c0r*pb;fi/ ,ms :t goun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3+lshx: g8)bh h), respectively. What are the components of the sum of these two veg l h:+h)hbsx8ctors?

  Two vectors A and B have components (0, 1koen ,vn l))qb*;1hv2 yr*w gu+slu4g) and (-1, 3), respectively. What is magnitwe ub* gu2h,v1lvo;)kqn+ )yngsl4r*ude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What i88c e2whxe,m95fhs o js the magnitudhx h8ojmw8 eefc 92,5se of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude qk+s gxx) r4: 0wyc2bbn /7dxiof its displacementqb:xi4/ g dxsy70wxn +b2 rk)c?

  Three vectors, expressed in Cartesian coordinates, aru(rtobffdu (qdh3,9te 6 ;b/ ke
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 coordip2nk o w /+x(rku)aeb:nates, 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 t+zxa42egm e: romr lq8op2*4zz4-o jehe magnitude of vecr2 eml4-4oq48ezemo xz*za+ :rjpgo 2 tor C = A - B ?

  A runner runs halfway around a circularouodgjvz ;rxgg:7 +2vw:4u4 g path of radius 10 m. What is the displacement r x7uuowgg ;vg: + g42jz:d4voof the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitu )p -u 3jnypy7zj7eh5ude of the resultanjehuj5u -)7zp3 y7npy t force?

  Two forces are acting ow.-labrygt7 93 f0h jwn an object as shown in Fig. below. What is the direction of the resul3 7rl wg9t.wh0yajf -btant force?

  Vector A is 3.7 cm long and points along the posi9ue6+;ew* tlcvx9am ative x axis. Vector B is 9.2 cm long and poin9u tlem*6xw ce+9;aa vts at $+51^{\circ}$ 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 73 cm lo/px+ b6:zlo ywng 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 35 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 horizonta8 g:)ioufz:tj kf,yf6 lly with an initial speed of 10 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 2.7 s. What is the height of the cl ,z)i:u6fty:o8f f jkgiff?

  A girl throws a rock horizontally, with a velo- yoafzsls-0 4zv)-bn city of 19 m/s, from a bridge. It falls 17 m to the water below. How far does the rock travel horizontally befos4vb y )o-afnzzs-l0- re striking the water?

  A ball thrown horizontais b**:brh kire e-)w2aw c).llly from a point 19 m above the ground, strikes the ground after traveling horizontally a dista*)-eiha)bb s 2ke.ir* rl:wwc nce of 24 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speedz5;kv0j 0/wev gzk 7fd of 12 m/s at an angle v;z0zvjfd0w7ke5/kgof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intoikf*-h rlw-nt u xxs/t/ -(sbpq(d/(a the jump with a speed of 12 m/s at an angle of ibhwd-tpf/n *q-u (k (a/sxlt/-s (r x$18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 39.7 m/s at anzn 7m it3qacie r ; c9pt-:o* jc,xwjhn*c32f5 angle of $13.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 37g ph(jpiiop*fyhvgut/42)i5n5 j5( e.0 m/s at an angle of $38.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at ) l1-xa7t;kc)cmmc of 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 bj2* k 9loola/ vw8,*n4;oqspc4ohnfhorizontally at 21.4 $m/s$ from the roof of a building 44.1 $m$ 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 sp ew6ub6kx s9xl 9slx8ca5w3/leed of 42.3 m/s at an angl ww9s6kl s8ex b39lcauxx65/ le of $44.2^{\circ}$ 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 c xl2vfg)u2av uqfk /qy9qnu.i83/an;an 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 slows your speed by 282 vu9).ql;n xff2q/yg3qa/ au nivk u.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 liwm c2kyxut* 5r+)mks4l2l6s4x 5obis in a wind of 50.0 m/s to the West. The plane's speed relativ52 wk)l5y rksxsm4 i* tx426loumbl+ce to the ground is

  A plane is flying due South (,s,.umszvu/f7 wti u .te 9z7f$270^{\circ}$) 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 1j (a enkae8r)3o,ba5f20 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 horiu:+ pq8k w uxr7t5xmt)zontally fires a projectile with speed 50.0 m/s in k x)r5 qxut t+umwp:78a 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 acrostm u dvzma3((:s a river with a currenta :d3(mvum(tz 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 15 m/s in still water wlvvneh4r6 k 86t ze4yhcg2 ly;m; )e1pishes to travel directly across a river 0.6 km wide ihgyytl m6 v1re4)8necv;;2e h pzkl64n which the current flows at 6.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in xyox8upjx+v1/; w wt . paejg s+e/m5)still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the dr+p + ;5p .vesmyw/wo/jjxu)agx81 etxiver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposi) mbbr k mxgim0m-,:*wte bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swimb: mmxi,) g0*b-wkrm m in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank1r4:xc v: p*rkcitb7p in 6 min 40 s. She is swept downstreak ppb4c7rc1 i rvt:*x:m 480 m. What is the speed of the current?

  A boat, whose speed in still wate:43o-uxv/jzrcgr : sx r is 1.00 m/s, must aim upstream at an angle of: suzxr:xcr3v/go - j4 $31.7^{\circ}$ (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)  $m/s$