Which one of the following is an example of a vector quantitv7b h3g q6jfh:y?

  Which of the following operations will not /- giixsxl x9t9o(, jhchange a vector?

  Which of the followingftxihe,**pej7hmloy i0l 2 ;4 is an accurate statement?

  The resultant of two vectors is the smalles (hr01fngcene*s x2f /t when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m aec 6j,-h6dixi t;bzxc0 :jy+) yy t:cug*q*ajnd 7.0 m, respectively. When these two y-0, azc u c: ti;6y+yt* 6cjd:*j)qixebhxjgvectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are zhvtkf8ra82ax 62n9f added. Which one of the following is a possible answer for the magnitude of h9fa 8x68ar zt22fnvk the resultant?

  Three forces, each having a magnitude of 30 N, pullp/2 ( ehrkisu8tm/;h e 6iqsg 8)ogdv9 on an object in directions thate9/q 8hi sgrev)i ;6h/k(pmt28gu osd are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is)hxm-q+* -lfoov z;on

  Ignoring air resistance, the horizontal c-6se/ *1krfr6dfnn q0nqq6iw omponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an axayt**gtz wg wdq*-22ngle 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 a6kv ac2l0q )rb projectile's acceleration0 a clr)k6bqv2

  A soccer ball is kicked with a velo ).ps-x, rdtsr0vq;d9xw q:6z ti/fkc city 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 ve9semchqyvb823l 6 y.octor of an object is directed anti-parallel to the velocity vecto.8ohe3 yb9q2c sl6ymvr,

  If the acceleration of an object is always directed perpend3mtoene 41lg-iwi9 c) icular to its velocity, ite)4migc3le- wo1n9

  At what angle should a water-g q1sr4zos-t xm5p t,hfjotg5jx -) v96un be aimed in order for the water to land with the grf5,qzgososjhm-t tvt- )x5x9pr1 j46eatest horizontal range?

  An Olympic athlete throws a javelin at four different+ ugki ny:b(f0 angles above the horizontal, each with the samef0u(ny bki:g+ 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 fmw0(/ foz t(nthe second time. If the ball leaves your hand with twice the vftw(m/ nf0 z(oelocity 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 8.h o;o8*v owjss(tld9o-mc2 6l0 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 htgwi0te,5o i*eight, how does its speed compare to its initial spee5 g0wt,tio* ied?

  A stone is thrown horioby czyyz 8ish;z;c:4o(3 ni8zontally from the top of a tower at the same instant a ball is dropped verticasy iz(8c8o i; zbh3nz4:oyy c;lly. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant :tggj1qi1cgmbo /1 rcbhc:/) a second bullet is dropped from the same height. Ignore air rr11cbi h: go /:qg/b)g1cjtcmesistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 45.0 m/s and at an dlro:z :3bfapswgqbu-k1* c-3,)ykyelevation of 128 m drops a package. 5.2 seconds later it drops a second package. How fa kqfpydzw)c*b 3kroas b uly-g3:-,1:r apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, ant7ng; 0 rscx d76tqw7kd one second later a second package is dropped. Neglecting air resistance, the distance between the falling6n gwdkrxc 7s7;tt7q 0 packages will

  A pilot drops a bomb from a plane flying horizontally at at(plkl(5zi3y1 1 hhy /ho j3ob constant speed. Neglectih5l3/bok (z1plh(3 1yjiyhotng air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Mnvuw(; +uen, 3np tvi6oon is only one-sixth of that on Earth. If you hit a baseball on the Moon wit3vn+ e uwun,v(6nt;p ih 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 relativeko4jok,zu6 / 3io7oel to a straight, level road and pass a cajk6ozu, 7ke4/ooi l3o r traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that fl tokn,deu1www d m3t54wh3r3 /ows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the wemwr35ndk,hd w uo/w 3 wt413etst bank directly west from your starting point. You should head your motorboat

  Your motorboat can mo*b7mb0bj 8uukw 4pt j9ve at 30 km/h in still water. How much time will it take you to move 12 km downstream, in a r b*jb40 pbu7k9 tmw8juiver flowing at 6.0 km/h?

  Vector A has magnitude 8nxib :1j:qxz 8.0 m at an angle of 30 degrees below the +x axis. The y componei1b:x znj 8xq:nt of A is

  If a ball is thrown with a velocity of 25 m/s at an angle 6bbzw;ptv ;t ,of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direction north of eastwbhi , :7phy8wdc 0*q-n:iiqi and you end up 2.0 km north and several kilometers east. How many degrees northwiin: ci7 qqby-i0,h *:hp8dw of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of itgoi:o6 1zv;z5m n ij0zs velocity is 8.00 m/s. The angle between the direction of its motion and the x axis mgi ojo :i61z5z0vz;nmust be

  A 400-m tall tower casts a 600-m long shadow j 7d4 irtgxs6fqf nngq )i;0l/x/f(4jover a level ground. At what angle is the Sun elevated above the hor iji;) gsx 7ffqtl/ng/4(n6d0rqxf4jizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. 5i vml8 l3j)4/fsfabbWhat are the components of the sum of thesll8j54 m viafbs fb/3)e two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3),co v c z:n8aam2yv1y23-j 2 vrelbq),y respectively. What is magnitude of the sum v,c )v3y2 o 8y2vyaelb qrnmz21j-ac:of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0ye; ak7 /i3g q-*lrl bhdu8-oy). Vector C = A + B . What is the magnitude ofd */uolie-y8k yar7 3qg; -hbl C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its displ)ofplz wx2-ii7k.+ hp *ixo.t acement?hx.)k7-il*ow .p+txof2zi ip

  Three vectors, expressed in Cartesia 5gf9nwis l926m fc)l/( iykypn 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 coordinatsfz 7jfdco)f/qtvou3,d1b -v. dmy1()7dnw n es, 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 = (+-x5 hnhnp;1qv3.0, -8.0), what is the magnitude of ;xhn5n1-v hqpvector C = A - B ?

  A runner runs halfway around a circular path 9zqww;1af )x-uehv+ o of radius 10 m. What is the displacement of the jogge wzwexoq+91u;- v) hafr?

  Two forces are acting on an object a e; /cs;8ck1wibkpf j7s shown in Fig. below. What is the magnitude of the ree wj;;ck7 s/bfk 1cpi8sultant force?

  Two forces are acting on an object as shown in Fig. below. What is tm.ekrl66gcv n2e 8;4rz(by-:ks ejgq he direction of the resul z4 -q:y k6. gr vekrm;cs8ejlne2g(b6tant force?

  Vector A is 4.2 cm long and points along the positive x axis. Vector B is v9)qeu; 3rt0v5( 9:jr iky9bwq ltluo57oulx7.5 cm long and lwkvrr 5oxt 59tuu7y eilvq0; l :j3ob9u) 9(qpoints at $+46^{\circ}$ 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 66 cm long and points atl5n4z9 vt(h ywdrb(p ./r v-sf $30^{\circ}$ above the positive x axis. Vector B is 16 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 29 m/s 4hjf v zw56iq116wg wliq 3md2from the edge of a cliff. A stop waw3 61 iz dv w1lm65gqqi2wjhf4tch 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 cliff?

  A girl throws a rock hon1*usz o gjr;v a(.g9yrizontally, with a velocity of 11 m/s, from a bridge. It falls 28 m to the water below. How far does the rock travel horizontally bjs1z9*oggr(yva. u;n efore striking the water?

  A ball thrown horizontally from a y- t 2wi;7g/wxlm0;sjqk gu29t7fjbt point 28 m above the ground, strikes the ground after traveling horizontally a distance of 22 m. W7f/g yubj-g ks9mlw w27qijt0t;;x2tith what speed was it thrown?

  A jumper in the long-jump goes into the jump 6/m)tyixere6k ;/9 bl xur k:zwith a speed of 12 m/s at an angle of me/b6 : 9riu)kl6ze/yk xxt r;$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the longezdm1r .o1v c9b,x* cp-jump goes into the jump with a speed of 10 m/s at an angle ofeox. d1cp9*v1 c,bmzr $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with c.rawyzx/+x .*2fo t xan initial velocity of 46.1 m/s at an angle of $17.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 43.6 0sgi+q ch -pnb*c -kn)/et8ywm/s at an angle of $13.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firbe)k// 3)wym1z cjn psed 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 shot horizontally adpkk 1 ox7s37ft 25.4 $m/s$ from the roof of a building 46.9 $m$ 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 46.3 m/s at asbz6*8e y; gqt; ck(m0w3waoin angle ofybeg6s0 3;8i (mqct *oww za;k $45.2^{\circ}$ 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 can run a 1500-m race at a velocity of 4.0 m/s. Ifw . nf/oj-;il8 8f4xm -pbd.n aapb7m3vww3jj you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the tijf-v 8 3 nj3wxwp.nb 8-awjf7a4./dimmblp;o me 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 50.0e55urk 41-po0ke e(whufl vj1 m/s to the West. Thejf4re wko 1h(5pl kuu-510eve plane's speed relative to the ground is

  A plane is flying due tld9g-9jw jx2South ($270^{\circ}$) 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 heg43 4cm o8r2 rqdszez p6()almaded $30.0^{\circ}$ 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 tbqj ) m qyt2oa1;d(y 1.qim6ufires a projectile with speed 50.0 m/s u1o( j62i).mqy dabqty; qt1 min 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 is 8.0 m/s, is direct6y+ m. ec-rk 43x6ikqa*psvl v;dbg 4bed across a river with a current of 6.0 m/s. What is the speed+ges.3r al 4xm vibcb4y k*-6qd6vpk; of the boat as it crosses the river?

  The driver of a motorboat that tn a p0689nkurcan move at 8 m/s in still water wishes to travel directly across a river 0.6 km wide in which the current flows at nna0pkt u8r9 64.9 m/s. How long will it take to cross the river?

  The driver of a motorboat thhzt8qdja- xmrb/c( q ;e*::+atv mn 1kat can move at 10 m/s in still water wishes to travel directly across a narrow strait in whid/b(vj+xzckm: -em 8q;tt:*h naa1rqch the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m ) .pmnquhq,,4vgmezzwg85 8sf d7du6 wide reaches the opposite bank in 6 min 40 s. She is swept downstrea68, n.5zzsh8g4g )wu deqq, 7fumd mvpm 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppositbq hxwm en2n72tya 3 l)9t3ws(e bank in 6 m (t79 qe32n)bwxmsa nyth2wl3 in 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.81sp.pq+avvyu- sn 9 p.pm7 78pk m/s, must aim upstream at an angle ofvsa7ypu-p8v+n pqksp p 7m. 9. $12.7^{\circ}$ (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)  $m/s$