Which one of the following is an example of a vector quv-px l+01dlzw m sahf. *q;,zs07ebzzantity?

  Which of the following operations will not ch1e-krgrde) 5z ange a vector?

  Which of the following is an acb /mapja5 uzep8/0s i;curate statement?

  The resultant of two vectors is the smallest when the(/ s1z:/sxo p -zfwumt angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectiv.. gvaiyvz5w.. )j jhxely. When these two vectors are )vwy..x5 g.zhijav.j added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followi(eik xgum91 2hgmlh+; ng is a po1gk +mu2i9g(e;h mlh xssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object iexbl y03v,g (yn directions tha0(yy,gx lve3 bt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown v 1olfo2 tfh m7xd6*e/oector is

  Ignoring air resistance, the horizontal component of a projectile's ir s8 oiw8,ih0velocity

  A ball is thrown with a veloc0ps +vi* 3qbfbity 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 horizontal component of a projectile's5,1z7rx3ej eja it5fs accelerationsite ,x5 1 3zr7e5afjj

  A soccer ball is kicked with a velocity of 25 m/s args-e n0 l3kq0j5 x7;r4ap xnat 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 tiup9p)1nf-o anti-parallel to the velocity ve1-t) in9opufpctor,

  If the acceleration of an object is always directogexedu h91g, t4 gth0g3 :c4led perpendicular to its velocitghd4c9g,1h: eex t3gl04 gut oy,

  At what angle should a water-gun be aimed in order for the water to land with6 cb6iqle .6mj the greatestlq e.66bjm c6i horizontal range?

  An Olympic athlete throws a javelin at four differ rkczx3(: jzi3vn(; ycent angles above the horizontal, each with the same cr(njic3:; vkxz3(yzspeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for+lequ6 5l-ldjib 35vl1r4lj 4*jgs ig the second time. If the ball leaves your hand with twice the velocity ij5 ul5*bg64lgqr ljl+e lj 1s-i3idv4t 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 8.0 m/s at an angn;flwry s6jo6s;z6b/7b . 1va;rvm ucle 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 reac9-mq4hzi1 o x.h;q xlfe:v0vlfz;0 sthes its maximum height, how does its speed comp4 s0x hz;emf9t iohl1;xv -:ql .v0fzqare to its initial speed?

  A stone is thrown horizontally from the top of a tower uu2t ft ygq8ko0v vg4/3u:0kiat the same instant a ball is dropped vertically. Which object is traveling o:tv28 tu04ik3k/v0uygqug f faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant an0 2 mh,pdf4hv;jb/yj second bullet is dropped from the same height. Igno jhb d2;n0,j/v hyfp4mre air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 89.9 m/s and vwv i oq/8hdsq+8q v89at an elevation of 231 m drops a package. 6.5 seconds later it drops a second package. How far apart will the two package qw/hq 8 9qsd8+vvvio8s land on the ground?

  A package of supplies is dropped fromyp i6b; los:w,ny:d 1s a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falliy 6 py:; ow1idns:,blsng packages will

  A pilot drops a bomb from a plane flying horibv de/q/ /.h7hcsa2ulzontally at a constant speed. Neglecting air resistance, when the bomb hits the grolvu/ a7/.h qhbcs2d/e und the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. If xvcbo h4./5naga tw0v .*;bnap8(zg tyou hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, th/vapo*vnbat.wc 4(t05gx a 8.hn;bgz e ball would land

  You are traveling at 55 mi/h in the +x axis reczvm -n9wr(t83dmsxa ur*j97 lative to a straight, level road and pass as zmr8ct d9auv(j nw-3*9xm7r car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that 49xitwwh*4vce wy :dksd55 r)flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shovd4wewt r*dk9:4 x5) c5iswh yuld head your motorboat

  Your motorboat can move at 30 km/h in still water. How much ti0fc1 b iuv(5xeme will it take you to move 12 km downstream, in a river flowing at1 ce(0i5vxb uf 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degreeu:fw1oy l vw08s below the +x axis. The yyv f08ww1uol: component of A is

  If a ball is thrown with a velocity of 25 m/s at pkaeom*r 5ho ;l((mk8an angle 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 east and zvx+(y (1xi) nmlgdx( you end up 2.0 k(di +xm(l1n(gv)y xxzm north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with -stag5/q b ik6a speed of 12.0 m/s. The x component of its velocity is 8.056a/k qigsb-t0 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casullky.5 q;zr c;*h lo5ts a 600-m long shadow over a level ground. At what angle is the Sun eleh cl5l lyrq;*z.uo ;k5vated above the horizon?

  Two vectors A and B have components (0, 1) afg moui)k,*+p3g3p ep we6h7hnd (-1, 3), respectively. What are the components of the sum emp,37 fhup*egp)w+h3 i k 6ogof these two vectors?

  Two vectors A and B have components (0,:c1b v slaxfob8y)p5, 1) and (-1, 3), respectively. What is mlx1,b)8cv:p o5sfby aagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B dq ,4/hodi0xn= (3, 0). Vector C = A + B . What is the magnitude of C ?d0 q/ ihnodx,4

  A car travels 20 km West, then 20 km South. yp;z :5g8/ v2rp nzyywWhat is the magnitude of its displacement?ngzw8pv: ;/ 2 y5yyprz

  Three vectors, expressed in Cartesian coordinates,:zvx* 3e3iglq 8 w5qas 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 Cv (i9tiyh5f3 oartesian coordinates, 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), wht).l:- w9.jdq c b;j3q *+cypacwsmw4ruy ; veat is the magnitude of ve).e:wl 4a;v cdpy9 j qucbt js;qr-+cww3.ym*ctor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is thmmnc ;dya 0 ;6azv8qj1/b 1mlre displacement of the jomyj 8/a;;q0 vnmlam1db6zcr 1 gger?

  Two forces are acting on an obaqeq p;icn* :9tm;m/g eq+ m+oject as shown in Fig. below. What is the magnitude of the resultan meeg;p/mm9* +;ao:qcnqti+q t force?

  Two forces are acting on an object as shown in Fig.oomy3k6oz j: ,*s3qxy below. What is the direction of th:63 osm*o3qkoxjzyy, e resultant force?

  Vector A is 3.2 cm long and points along rz 7 hwq5n:)eic6fs r kh60rlsw,j ./othe positive x axis. Vector B is 10.0 cm l/kc7 q zhw, .l rjh)rsoer:sn0 566iwfong and points at $+37^{\circ}$ 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 90 cm long and penmob 2z o2wn02e wdhil47xu+l( l.t (oints at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 28 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 22 m/s from the ed3- /n-fker kbtge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.1 s. What is the height of the c/ bek-f3nr- tkliff?

  A girl throws a rock horizontally, with a velocity of 15 l )mwlrm;e5y0 m/s, from a bridge. It falls 27 m to the water below. Hom; ey0 lm)5lwrw far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, strikeyhioq co8vql96y n9; :s the ground aq;o6 c:vin89qyyh l 9ofter traveling horizontally a distance of 17 m. With what speed was it thrown?

  A jumper in the long-jump ly5ws r 62ylo7goes into the jump with a speed of 12 m/s at an angle of l6yw 2 5yro7ls$20^{\circ}$ 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 syicuq p ;ai07kp z18f*peed of 11 m/s at an angle 1y*0q 7ai8kp fuip;czof $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initialqkb + 0c43b ha)n-enff velocity of 55.4 m/s at an angle of $42.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with i,aog1 ah0cfy1g/t9wxmg 4s :an initial velocity of 29.0 m/s at an angle of $32.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an a.( c- mi 5v*eggf8dvebngle 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 horizont7ep)bj2 7 qeigally at 21.9 $m/s$ from the roof of a building 35.0 $m$ 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 greq1f,bb 4+f vapc-uhd dh3v hw1 gc116ound level with an initial speed of 53.0 m/s at an angle of d1+fe ,v3fh u4qgc b1h a- wpvcbhd161$39.1^{\circ}$ 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 runes l2khh,p d-ifd (j53 a 1500-m race at a velocity of 4.0 m/s. If you ran the same rahsl(i2-3,f hk 5d epdjce 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 would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/sg 4nhmebem *(7b zll,o :h(gn: to the West. The behml,gn7::*eng l(m4(b oz h plane's speed relative to the ground is

  A plane is flying due So*ivacku: 1qi-4vpep6 uth ($270^{\circ}$) 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 1hh-t o0o)p,7w)n8 ynbdb j ;bq20 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 horizontally fires a po- ztuzydg ;:5civ7u-rojectile with speed 50.0 m/s in a forw votyg-cd7z:-;z5 ui uard 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 across a rive+gqs-ohmw+ ml 1 e+hw+qtsi-)6 pbrz6r with a cursp gose hz q+ -h+6- )mq+lw61witmb+rrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat t uxk. / li2.38k6ju, (nwdhm :vdicjlohat can move at 19 m/s in still water wishes to travel directly ac/n2u v h.k cj(o ximl,6d3lw8. d:uijkross a river 1.0 km wide in which the current flows at 6.4 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trajv b436z wfvg8 pnoi61vel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle ujbzv4 6n138 wpv6 foigpstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank iilnir .bm2nf: 06 sp0 2rg3syan 6 g2imrn6 slbn0f :sy 2pir.30amin 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directl 5ty2(sks1huiy across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed ofysut1 i( 2skh5 the current?

  A boat, whose speed in still water is 1.00 m/s, must aim upstream a ;t 3 3tse /eylj5k)abr3bfz:it an angle oflyza)setik3j3e3;rtb5 :fb / $26.4^{\circ}$ (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)  $m/s$