Which one of the following is an ex7g0vag,-w i2p bz-bb fgt)c9xample of a vector quantity?

  Which of the following operations will not change w. 4*t6k jclgza vector?

  Which of the following is an act 0 vsusi(p)t,curate statement?

  The resultant of two *d+gd a e9tmk(8fh5 z- oso,agvectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m/tzz sn,0pyp y.k2k (m, respectively. When these ty/p(tk . yzsp2m0nz k,wo vectors are added, the magnitude of the sum

  Two vectors, of magn1ow 1l oo4:,vd0ddzxbitudes 20 and 50, are added. Which one of the following is a dod1 1vxl,0woozb d4: possible answer for the magnitude of the resultant?

  Three forces, each having a magz b m2pfkmgtpn 6t(q+r1auha15: 6l-fnitude of 30 N, pull on an object in directions that h15qtp+62 fgftmz aark:1m bnl 6(u-p are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unk 5qt,wjy 9ihi+nown vector is

  Ignoring air resistance, the horizontal component of a projectile's vlihppdbj iv /*k34h/oj*:)7 jfh- qq yelocity

  A ball is thrown with a velocity of 20 m/s m23i l:r n5ajeat 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 comz vg-qi caqwm,r1ml/y6 z;7k*ponent of a projectile's acceleration,-m7ia6;q gy /lw1 rv *zmqckz

  A soccer ball is kicked with a velocib 8wdw 0sd5g;g7aj i0n-z(dtb ty 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 bhel:sd5i 42m object is directed anti-parallel to the velocity vect:eh li5d s24bmor,

  If the acceleration of an object is always directed perpendiculaeieoba8n +/g.o0q a w,r to its velocity,eo , iaw08.n+aqe/go b

  At what angle should a water-gun be aix ohrb7sc t zgf*h.ax8e-. g:.med in order for the water to land with the greatest horizont.et o: g.hr.8x7*gfxcsah -zbal range?

  An Olympic athlete throws a ;9w fqtj y9+ipjavelin at four different angles above the horizontal, each wi +;wfjy p9itq9th 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 for the second time. If the ball leaves you 0.,dzl)oksa ur hand with twice the velocity it had )doz,la ks0 u.on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at anuniw .1jp( flo10t+t,cjs 2 or 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 do16cn(tqp 9f)ll7j rnc 8zkhk;:wan t 1es its speed compara6z; 7 jnl(8 k9h:l1qkr1)tnctnfpw ce to its initial speed?

  A stone is thrown horizontally from tqlv1 0e ,)xxutrj7yvi l mh94/he top of a tower at the same instant a ball is dropped vertvx90lvmyut )r,j41q7e x/li hically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired ho9:0k.pmxm3cw kwqt7su6 -ksurizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the twotcwpw6m k0smk7 xus: . qku3-9 bullets.

  A plane flying horizontally ab8jpn7kc92 8l ztq q*j+t9p+xrl k2opt a speed of 120.0 m/s and at an elevation of 220 m drops a package. 4.6 seconds later it drops a second package. How far apakoz tj++*l 9tbl9krqp7q2xp 8c 8njp2 rt will the two packages land on the ground?

  A package of supplies is dropped from a plane,cgm8v+ir ix; jr-+3vs and one second later a second package is dropped. Neglectinm; 3+jris r+vxig v8c-g air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying ho4bu 6e y rs(vay7ye3b+rizontally at a constant speed. Neglecting air resistance, when thb+ rua7yyye3 e( sv6b4e bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of o8g9- -zkq.9il -6soiou exqe that on Earth. If you hit a baseball on the Moon with the same effort (and axzel6 -uiiq-g89 .q9- ooes kot 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 straight, level r fjj28zr:()r sewv nqj-4gvdz/,8*szte:a m a oad and pass a car traveling at 45 mi/h. a e2vja -zzrmfwrd j *jznqs,gesvt :4:/(88 ) 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. You1k-,g m zpgw+r start out in your motorboat on the east bank desiring to reach the west bank directly west from your starwpmgzr +1g,- kting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still wa/+jrv x- )3j3d etjglyter. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 je/-xtg)jv ld+33yj r km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below l(3hx qc s2ua3the +x axis. The y component of A iu(q3ah23 cls xs

  If a ball is thrown with a velocity of 25 m/s at an ang6bep6 uqi- m8wk1tlr +le of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a stra9 zqr-w.o5 qipight line in a direction north of east and you end up 2.0 km north and several kilometers 9iqwq5pz.-o reast. How many degrees north of east have you walked?

  A butterfly moves with a sp 8l -cjconl( bfw242sbeed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle w (2sc- 28fbbjn cll4obetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600j;k )fotq+u) u-m long shadow over a level ground. At what angle is the Sun elevated abovetu )kjuq+o f); the horizon?

  Two vectors A and Br7tr3k9r;mt f have components (0, 1) and (-1, 3), respectively. What are the components of the sum ofk 9ft tmrr3r7; these two vectors?

  Two vectors A and B have components (0, 1) andhhjt qz ei(8y ),ft)d8 (-1, 3), respectively. What is magnitude of the sum of theset ),d ti)ef(8 hhqzj8y two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitudw7fi+np6yln/l60 u p2cvf s8woxf*b(g2lu . se 20p lion* x(gcuv 8 .6+ny7f/lwlfpw 2fsu6sbof C ?

  A car travels 20 km West, then 20)vwwp*vbu :okl 9j8l* km South. What is the magnitude of its displa9v*w uw o bp*8l:kvj)lcement?

  Three vectors, expressed in C+y6gu3w1ln lk omn, 49jrmah :artesian 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 coo56fb p79.att/zylc t grdinates, 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 it bu3()efjvkq*cj4lk ;7v v5 ds the magnitude of vectov5 )qbk ;jkul4tv3jvfde7 (c* r C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is smhp 1o) p1a1kul1gc* the displacement of the jogglgpa )uho1p1k1* 1sc mer?

  Two forces are acting on an object as shown in Fig. below. What is the magnitqi 4qlqchbw3 z1(6e,vude of the resul6(1q icwvbq lez43hq, tant force?

  Two forces are actingn802fsyfmqs /0nxqb osn/; 4p on an object as shown in Fig. below. What is the direction of the resultp nyss x/0bmf8/; f40nq2sn qoant force?

  Vector A is 6.0 cm long r qw nq8:u,q1),2 d2b:ycg(bze o hpsrand points along the positive x axis. Vector B is 6.6 cm long and rbn 2ohrq)g(y2uwp q :cd1: sqb8ez, ,points at $+41^{\circ}$ 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 55 cm long and point m(q0aj ;dq 636lckusa4n+igss at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 33 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 20 m/s from the edgehw6gu53uy 2yz / vbnl/ of a cliff. A stop watch measures the stone's trajectory time from the topg2/n65 3/ bzuyw yuvlh of the cliff to the bottom to be 3.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bri3pc9 t+6 xuxlhe7hv )zdge. It falls 20 m to the water below. How far does the rock travel horizontally before striking thu9)te7hv3 h6cxz xlp+e water?

  A ball thrown horizontally from a point 29 m a)cg*n wak9r0xpd kz 8+l7afh ;bove the ground, strikes the ground after traveling horizontally a distance of 21 m. With what speed wawxa gl )n+ ;7fkkdharp 09z8*cs it thrown?

  A jumper in the long-jump goes into oln09*/xy k0x+lbq w qlq9-qkthe jump with a speed of 12 m/s at an angle obk0 +q*lqkx/ wqllqy9n-90 oxf $20^{\circ}$ 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 spee6 lwnnfa f;/ 8vt9mbt5d of 14 m/s at an angle ov b t /t8wnlf5a;6mn9ff $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an :u; batbtj h j*.rp6p4initial velocity of 50.6 m/s at an angle of $28.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 43.6 m/s at an angl v -/sqmc22 ux:3.dqpku1g xiqe of $34.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle pv7/s.b/vyr(v)xeb oof $30^{\circ}$ 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 horizontal2o/ houfi(.m ue0god3i7ib5l ly at 16.9 $m/s$ from the roof of a building 46.1 $m$ 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 gf 42zz *swlb3 gbm.zd*round level with an initial speed of 45.1 m/s at an angle o *.3b42sbwzzf*dl zgmf $45.5^{\circ}$ 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 rym9 ;q:wx wwoz)ucw0etct nv1l.)9e1ace 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 2.0 m/swoze9v tm1 9wy.)t l0c1:q) u nwewc;x, 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 wind of 50.0 m/s to 1q:yya *k7ymqa a26x (s2u oddthe West. The plane's sady (aq1qk72yyom 62xd: sua*peed relative to the ground is

  A plane is flying due Soutup(i.o ug r.,skctcyycw o*0 1:/1ukqh ($270^{\circ}$) 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 sp* 9z03wu6:xb;vgoee*u y hfn weed of 120 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 horizontallk*cidr o3p enl;/9vu r6+d6a ay fires a projectile with speed 50.0 m/s in a ek9cp/*6r+dar i 63dlu;von 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 isu7o0vb6p*rum:gu lj+vvro 2 8 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the sp*vpb+ugrom 82u0 7j6l:u rvvoeed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still wa*dv 4g3;.h iedxy;tk q 3o:tskter wishes to travel directly across a river 0.7 km wide in which the current flows odh *3t4ekiyx3qv tk.: d ;s;gat 5.2 m/s. How long will it take to cross the river?

  The driver of a motorboau uqk9.pt:2dry8-xn st that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. tx9.sr:d2kq8-p y u un At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reacvquzvs7q(1k*jr:pq 4 hes the opposite bank in 6 min 40 s. She :1p(jzvrvqq s*q4ku7 is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rivtqy4j) c 7chj8er 200 m wide reaches the opposite bank in 6 min 40 s. 84ycq)jcjh 7t She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.4jql5 zc.vcjv;3 bb2 d19 m/s, must aim upstream at an angle of v3jvc4dc;j2 . 5bbzq l$28.1^{\circ}$ (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)  $m/s$