Which one of the following is an example of a vector quan;xc )xh gnqzv9d:tnlv.ls ;(c/;0 m hwtity?

  Which of the following operations zyw+: :7te-p3ouj pw twill not change a vector?

  Which of the following is an accurate stat(2rb3 o +whp.dgcnpz.m 0nd9iement?

  The resultant of two vectors is the smallest when the angle betwf/ppy)itd/1 ween them is

  Two displacement vectors have magnituce7+9 au6d n i0;ainfwdes of 5.0 m and 7.0 m, respectively. When these two vectors are added, ufi adn e9c7+a6w;i0nthe magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are a 0j+l)o,exltv dded. Which one of the following is a possible answer for the magnitude o+lv x)t,ljeo0 f the resultant?

  Three forces, each h / ,bh 98iymx2s)k74gf lglgtraving a magnitude of 30 N, pull on an object in directions that a2y7l48mt g 9gxh, g fkib/lsr)re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowac*h*, 2b kbz8-s2rny mwrfz 8n vector is

  Ignoring air resistancjq lgop0zyf d3k.gt9-g)8k1te, the horizontal component of a projectile's velocity

  A ball is thrown with a velocic+.two( wqep 0ty of 20 m/s 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 horizont+ u9-ds.16mawwf (fl*y3 uv-d ) onkift2 iopbal component of a projectile's accelerationu*(u)ft6ndi -vbifk wmaoopl 29 dyw+3 . sf-1

  A soccer ball is kicked with a velocity of ci02y6 +ztzca e0a ai*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 directed anti-( j;qfsh cp:sw./q w9)ddfz9rparallel to the velocity vector,pfrh;w (/:s)j9.fcdq 9w szqd

  If the acceleration of an object is alwaysl:u) ul a*sfj8v mt+nwyy5vzy4 ej+1/ directed perpendicular to its velocitv:v*+ 5)eltyulmfz/yasjw+81y j4uny,

  At what angle should a water-gun be aimed in order for the wat.l+gz3x m9e n i+z unag18adf+er to land with the mn.+9+z3eu8 lga1zixa +dfnggreatest horizontal range?

  An Olympic athlete throws a javelin at four differents5kqb ik(n4 ,g angles above the horizontal, each with the same nb, 5i4kgskq( 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 ;uz1.j( wvm2qkb hs+c 29so5ei- nffewith twice the velocity it had on your first throw, its h2ijh +-c5su. mose zffb;2q(9ke nwv1orizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle o:5bryks4 rt )sp8eb4ef $35^{\circ}$ 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, ho- hosym2cy mm19+ )ifqw does its speed compare to itm +9s y-m1)m2ioy hqfcs initial speed?

  A stone is thrown horizontally from the top of a 5qf5fpzkx(yxd* . :vitower at the same instant a ball is dropped vertically. Which object is traveling f(5d.*f vyzqi :5 fpxxkaster when it hits the level ground below?

  A bullet is fired horizbybv8v3;)kma -dq c9 oontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the tw3ob8vv k;)ay - bcm9qdo bullets.

  A plane flying horizontally at a speed of 103.7 m/s and at an elevwg2 v/7az;u.e g:wm md fyie*9ation of 179 m drops a package. 4.7 seconds later it drops a second package. How far apart will the two packages land on thew9/wd7 emvgug;ef2: ym.iz*a ground?

  A package of supplies is dropped from a plane, and one second later 6p9 gukv lth;:p6xdw .a second package is dropped. Neglecting air resistance, the distance between the falx;.6t9dgl vw k6:puhpling packages will

  A pilot drops a bomb from a plane fl5y7zyb.wf1xh hzsz+/ying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location / fh1 zbxwysz+y.7hz5 of the plane will

  The acceleration of gravity on the Moon is orvn*qd ;l.c)q nly one-sixth of that on Earth. If you hit a baseball on the Moon with the src. ;) *dqqvlname 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 rennfcy06x3aiq f0:tlr60 a*ie lative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the oth *006yarclxetni:ffaq0 6i 3n er car is

  You are trying to crossz1op 0ioycj 1- a river that flows due south with a strong current. You start out in your motorboat on the east bank diz c10y-1 oopjesiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. ,r6lhnc3va8 y(.kk lh How much time will it take you to move 12 km downstream, v nlky,hr8kc(3a6hl.in a river flowing at 6.0 km/h?

  Vector A has magnitude4 p dyp;stc7*v 8.0 m at an angle of 30 degrees below the +x axis. The y component ;td7vy*4s ppc of A is

  If a ball is thrown with a velocity of 25 m/s at z**j. p -yeyupan angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straion ,/+rf.a/4o8uurlsnal h:a0fjt9pa * s-t rght line in a direction north of east and you end up 2.0 l+ 9a,n. 8o:rosuf -jtar/r f04huatpa*n/lskm 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. Th( o/r tb2ka.juj yx4s5e x component of its velocity is 8.00 m/s. Tys4 kj5t2x (rbj .u/oahe angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level gry cje/ 80mfj+ x6qvv-mound. At what angle is the Sun elevated abovev+vx 8y6ce/j0j- qfmm the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What cx2.rl4uh o,i are the components of thex,.l 4ciur ho2 sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiveluf+e- rlemn 38k- 7cfoy. What is magnitude of the sum of these 7ulk+ -oerfm8nfe 3-ctwo vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitudqjl( vi7vh),q9z0 jd ze oflvv 0iq7dj,z)9qhz (j C ?

  A car travels 20 km West, then 20 km South. What is the magnitudyaqznyac h31tq1f2 . y d/5mp2e of its displacz /ya qpm 12 yf3ha25dq1.ycntement?

  Three vectors, expressed in Cartesian ci*x vz.zz:ev3 oordinates, 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 coordi: 26mpht+ jzt uqq9yhc33 9sdcnates, 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 zw83yj qcs is6x94cmonon /,3 = (+3.0, -8.0), what is the magnitude of vector C = ,3o3s8c9ozn4yx6q iw mc/jnsA - B ?

  A runner runs halfway aro.1ku q bcbj7ad2)wtu /und a circular path of radius 10 m. What is the displac /2cuta7b)qbkw1dj u. ement of the jogger?

  Two forces are acting on an object as sho4v4,cspmz 1 jiwn in Fig. below. What is the magnitude of the resultant fo4 ,4vpcz i1jmsrce?

  Two forces are actingkgm).se6 adxw0p5 g-d on an object as shown in Fig. below. What is the direction of the resulta ead)kgspm. dx6w-5 0gnt force?

  Vector A is 5.1 cm long and points along the positive x axis.*t bjqf04r,beo; an8i Vector B is 5.5 cm long and poa,e0bq *rb n;8tfo ij4ints at $+20^{\circ}$ 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 and points qh9q1/4revv q-*rgwn at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 40 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 hori ; c(y4bud8zxtkecac o ,3xa:6zontally with an initial speed of 23 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from thd :ckxxayb4eu(ac ,3t6 czo8 ;e top of the cliff to the bottom to be 2.5 s. What is the height of the cliff?

  A girl throws a rock horizont7.s qhimq;8apsl+u * yally, with a velocity of 9 m/s, from a bridge. It falls 16 m to the water beloihs7 8l ;umqyqa.s*p+w. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontall5gxzc9u 1:uqi y from a point 28 m above the ground, strikes the ground after traveling horizontallq5xc :g9u1u izy a distance of 16 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spee.4yk9f u-s xpao,+ onxd of 12 m/s at an angle oxauy o+o fp.k xn9-4s,f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpmzg cn t444+9qwlm/d vmu:v.z goes into the jump with a speed of 15 m/s at an angle z/+ 9: mg.4mlvnd cvzwmq44t uof $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 33.2; e-lq ji4/dozzo*p7f m/s at an angle of $40.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial xzxw/ x)6x -yxvelocity of 40.0 m/s at an angle of $48.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofx5u2+:s ggznr jr *xx2 $30^{\circ}$ 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 at 19.6 .m fh7-mcp-m xzg3ii0k6o4+hdonms5 $m/s$ from the roof of a building 52.3 $m$ 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/))z5hf, ospmmsvc 4kl4q0vq level with an initial speed of 64.8 m/s at an anglep msk v 0v)z)msf,4oq4/q5lh c of $43.0^{\circ}$ 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 vey vsr*b ltym2s)bz i-;:k 2g)llocity 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 ybltmkbr z2gs i )yv);y2ls*:-ou to finish would be

  A plane has an air speed of 200 m/sc3 3 g* hgp5gk:u+fvse1 ousc)w4(fbg due North, and is in a wind of 50.0 m/s to the West. The plane's speed recsekobs4p : 3) +uh1wgvg f5(*f gucg3lative to the ground is

  A plane is flying du* nwp,kw9 :dru5ow9)gos altl8 ait3- e South ($270^{\circ}$) 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 he xul: :9 :2snr6b+cb,kwshnozaded $30.0^{\circ}$ 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 mx2j v4lj1 4qd0zcj( w)6yjicz/s horizontally fires a projectile with speed 50.0 m/s in a forward directi4j(yjdwqil c1 0vjc jx4z26z)on $30.0^{\circ}$ 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 i5d/+mp+ bzr crs 8.0 m/s, is directed across a river with a currec+rmd /zr+5 bpnt 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 13 m/s in still waterg kawg+p50g z, wishes to travel directly across a river 0.9 km wide in which the currzk5a+ g0 ,wpggent flows at 3.5 m/s. How long will it take to cross the river?

  The driver of a motorboat th 5aavjk1e mh 3n 92)gzap6qh7lat 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 should the driver head g9jka53zlv7 qa)1hhep am2 6n the boat?

  A swimmer heading dir8olfz n7mmt d(.n .aw1ectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stilldn z m(7m on..f1l8wta water?

  A swimmer heading directly across a river 200 m wide reaches the opposite c+dzgddve11 y9ld* ;hwb6ol1z,ta3k bank in 6 min 40 s. She is swept downstream 480 a1tlv 1y 6 d1b dzh3wddgezkcl,+ o*9;m. What is the speed of the current?

  A boat, whose speed in still water q-;x ;cevf+(0odc,gjv+w :smou rqd. is 0.86 m/s, must aim upstream at an angle ofqq;+.+(dcjcs gv,wox;vu-od0 r e:fm $24.3^{\circ}$ (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)  $m/s$