Which one of the following is an example of a vector quantr,sb 1 m0k7 9vvswou/dity?

  Which of the following operations will noti4:n7;o (3z tms/r ozj)l,kdasv ni1y change a vector?

  Which of the following is(*y f+zr*i1 u bjcgwae fku80/ an accurate statement?

  The resultant of two vectors is the smallest when the ang 9ws-s y91bztwz9kq lj;(n kn/le between them is

  Two displacement vectors have magnitudes of 5.0 v pv*mu t;: zs60hpb1zm and 7.0 m, respectively. When these two vectors are added, the magnitude0;b pzvmzp:hv6 1* uts of the sum

  Two vectors, of magnitudes 20 and 50, are added. w * v:1q5mr9 stuati*e Which one of the following is a possible answer for the magn5mw r e 19t*svqu:tai*itude of the resultant?

  Three forces, each having a magzp8 c)fj4fsap o(i(3u nitude of 30 N, pull on an object in directions that aro( pij 83)sacpffuz(4e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector iserv(uc5w2x-hyxx 38y 00ye(xti l (gn 0 lb,iv

  Ignoring air resistance, the horizontal component of a projecti),phn 4ozg p9cle's velocity

  A ball is thrown with a velocity of 20 m/std8g h5n+pp(v, hjit* 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 resistance, the horizontal component of a projectile's accelerationz7tfr:; j8kwd;dzk:8j tf7rw

  A soccer ball is kicked with a vel)socqs.t r*4lpulr jd/22vn )ocity 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 din3golp z/*cd0q-stqqpln58 kv/ of50 rected anti-parallel to the velocity qq0t 35o*plnd/gzs 8vnkqcpf05ol- / vector,

  If the acceleration of an object is always directed perpendicular to its velousch./h+kys e*;7 n5 yz :nskmcitykzn y;7n yhsh:muek+sc5*s/. ,

  At what angle should a water-gun be aimed in order for the wk)5/)nf+a6arqe x a4j2okk yfater to land with the greatest horyfk5n 2je kqf a4x/6)ro)+aak izontal range?

  An Olympic athlete throws a javelin at four diffem*k 2nnh.ukk* rent angles above the horizontal, each with tn hnk*kuk m2*.he 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 your hand wi 7i3z9ahy) 6savu95depoge )w ,pet 0eth twice the velo)9oae pw65 zvgte h),90ypdi7eus a3 ecity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of m*)-pmwpg4iv/j bn)6owze i8 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 does0xji,t +i 6oc emm5hq4 its speed compare to its mmqoi6i+5,t4cj0 h ex initial speed?

  A stone is thrown horizontally fromzhqy*rgx:p31r +p q+ m the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster whepp+y3h1 xqq:* rg+mzrn it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet pel. nbj*9kd/o/,frm is dropped from the same height. Ignoree b/pn9r ./kfl omd*,j air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally wbh:xoua19y a6e94 vhat a speed of 111.0 m/s and at an elevation of 225 m drops a package. 5.1 seconds later it drops a second package. How far apart will the two packages land on the grou:wah9ye bvo94hau6x1 nd?

  A package of supplies is dropped from a plane, and one second w*k(d+1 drsv z*ofq;elater a second packsodwv+ (r;f *1q*ze dkage is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizoncpo;ds 2 w (qyv4qpt(e(4k;p,i e zm4mtally at a constant speed. Neglecting air resistance, when thee wmi,y( tpczdvq42 m4q4op s;(ke;p( bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on taad3ix) 0p8cs*mio 4 Earth. If you hit a baseball on the Moon with the same effort (ands )p0cd*3a8 atim o4ix 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 straight, level roadg5+pv44w8m, fjkm bf;yz/oecg)l,hk(o b z) s and pass a car traveling at 45 mi/ fzejz cf+4)owskmyl/k, hgb);p48b ov 5m, g(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 strjiaf8x *r4blwx*pg r34;4dw pong current. You start out in your motorboat on the east bank desiring to reach the west bank directly wrx8*wplij3fd4 w*x;r4 pgba4 est from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time wi-ktnm;33 .rrxe lvh x:ll it take you to move 12 km d3x tr-l:r;xe .hn3 mvkownstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thn:g k zri9 vs ssn/x98k.jfnr77l w77te +x axis. The y component of:8 f.7xkv s sstnkwigrr9l7n/nz 977j A is

  If a ball is thrown with a velocity o oon)xa iz5k37.(o udvf 25 m/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 straigak(kro z +:,bcht line in a direction north of east and you end up 2.0ka(+rz boc:k , km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The xk4m;2f))2j7 nc lhykdd b6chtr na):q component of its velocity is 8.00 m/s. The angle between the direction of its:); c4dmt2)nkcdalj q6 )72yhnhrfbk motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level g/9ynk lfk6(v yround. At what angle is the Sun elevated abo( 6y9/ knfkvylve the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What ko hc+l s:1f7,lqu5fgare thoh q7+ k5f:l,1fulc gse components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-(q dz.jrr9-lc-yi8y v 9w g+rx1, 3), respectively. What is magnitude of the sum (y wr.xqrid-y9-9z v8cjl+r gof these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is3:in .wehevl- 5cqp19jxlhda6e 4 db+ the magnitud eh:d+bd 3a.hn-jix q1w4ecvl le59p6e of C ?

  A car travels 20 km Wo44a: 6fcoa8z ;:bfqtj7y ln;iq5w w lest, then 20 km South. What is the magnitude of its displacemen;b zfo6l aqyw47wn;i8af: :4t5qj l cot?

  Three vectors, expressed in Cartesi;lta9bs/, h pav3zoj,an 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 coordinateqc y4m4x ispn1a,bk:kv )*j6ws, 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, n8v0gaakvyzkur 6umf*h6)6i m,1,ph -8.0), what is the magnitude of vector C = Avrp66*nu 6vfk ,h8i zmhaka 1yg), mu0 - B ?

  A runner runs halfway around a circular path of radius 10 m. 5gdnv.kkf7tu58ypfet - 2x9m What is the displacement 25ft8kvnud p75-f kyge 9.tx mof the jogger?

  Two forces are acting on an object as shown3lfzdz3q4j1q vpew80 in Fig. below. What is the magnitude of the resultant forq1wql vdf 4p083ez j3zce?

  Two forces are acting on a a2.f 3iaj4xq xj)m6 *idikh7un object as shown in Fig. below. What is the direction of the resultantdax a*qj7f4 )6ik3imhi xj.u2 force?

  Vector A is 4.5 cm long and points along the positive x axis. Vector B is 7.3 tre7r j;pxp5*4i2rdj cm lp; e 5t*j7r4r2xj pirdong and points at $+29^{\circ}$ 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 69 cm long and powh:xb89 dd8s aints at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 37 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 ofwm.)n2e io w(t 27 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 4.8 s. What is t oit.ew 2nw(m)he height of the cliff?

  A girl throws a rock horizontallalwz/nr7 m3o1y, with a velocity of 16 m/s, from a bridge. It falls 18 m to the water below. How far d7z 3lano w/mr1oes the rock travel horizontally before striking the water?

  A ball thrown horizontally from /j r1 ysu1izv26c/ye9ujb2sy r /xh) ha point 21 m above the ground, strikes the ground after traveling horizonjz6c/j 1 9/2yy2s1s/iehuu rxrby)vhtally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes int+eq + ;7p 04x iq0mtclblh6ysvo the jump with a speed of 12 m/s at an angle of;l i0c lx+eb 0 hqpvm7q4t6+ys $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goesf73mshzx(h) y2vo7d a pq/vx3 into the jump with a speed of 13 m/s at an angle zohf)x7mp37 v3 h/q(dv2xay sof $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 32.0 m/s at an b71 q7zutd,im,b dcd6angle of $11.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initia 2 xeo+o) e)uji*hs/szl velocity of 24.3 m/s at an angle of $48.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fira6zv/ pvkqi h ))(xoa9ed 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 shotrjudp89 05qjo horizontally at 26.7 $m/s$ from the roof of a building 63.3 $m$ 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 46./(m,k*bf. kemg jx wi:6 m/s at an an(f */gxjmk i:bew,k.mgle of $39.4^{\circ}$ 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 a6 z: 4qsxihn,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 2.0 m/s, the time it would take you to finish wox a:6z4n ,hsiquld be

  A plane has an air speed of 200 mgec)zs 1) 0mmg/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relatigc )zmm 01seg)ve to the ground is

  A plane is flying due Souy) l0,s2o prxc i2f1t-qcd ;lcth ($270^{\circ}$) 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 headk0 +2tibsw80u u qtf.ved $30.0^{\circ}$ 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 horizontally fireszev6zkipd3;7b pbww)hq g8 6+ *,wzdf a projectile with speed 50.0 m/s in awwb, h*6zve;w dp 8zg+k3di)6bq zfp7 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 w12: ibgsb/ dfvater is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the /db gvsb2 f:1iboat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still jq59c b e0;vdhwater wishes to travel directly across a river 1.9 km wide in which the c0 hvdq 5je9;bcurrent flows at 7.1 m/s. How long will it take to cross the river?

  The driver of a motorbo fdb.7:1bey/f 5dw vsjat 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. At what angle upstream sho/:fy7f.vew51 jbs bdduld the driver head the boat?

  A swimmer heading dikr 5 b* c+nmqk571wbjdad 1qy7;wfx2zrectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swwd7f2+zk* dr;1jqk nb bwc5 7mqayx15ept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a ridj3eft h/x6izcizvh0o.z ,7 ;ver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480i, dzi0/z x ovefh;jhc z.t376 m. What is the speed of the current?

  A boat, whose speed in still water is 1.39 m/s, must aim upstream at an anglxk),d3 3g-sup:p y7dzl8ifg ke of yl:-pg, zx3dgd3 kfp)8iu7s k$25.4^{\circ}$ (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)  $m/s$