Which one of the following is an example hm88qc;mh7(j8tc( ftxpz e9 p of a vector quantity?

  Which of the following operations will not change a-pu1.4u4 my:tpwzsi a a. ups7 vector?

  Which of the following is an accu4y39 is. d,zlui1rhjarate statement?

  The resultant of two vectors is the smallest when thear, xj*y fe o:w3 zrq:fo5,.ap angle between them is

  Two displacement vectors have l7vduy-h (lc r4of1: nmagnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are addedc:l7-l4dvu( nhyof 1r, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which on8ve2 bc8 1cw6zq*9lmc uemx4ue of the following is a possible answer for the magnitude of the resultan41uc 8qz*xm8c2lmcvbu6w ee9t?

  Three forces, each having a magnitude of 30 N, pull on an object in directionl(nae i 5wn25qs thaia5 5nwle2qn(t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, t*( bvcv7bh8az6u(e c fhe unknown vector is

  Ignoring air resistance, the horizontal*nff+zp/+ ld t component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an af)yc g06m y ; 5/k jgom.fvnp9w1-aekongle 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 componn- dsroq ,ztw+2m,:zew/ .o ksent of a projectile's acceleration, soq2 ,-r/ : zwo+zd.nwmeskt

  A soccer ball is kicked with aimp85isv8kur: yu5 b. velocity 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 vectolft krnd; :t7i+fsg+3 r of an object is directed anti-parallel to the velocitys7 +;ldi:+nkt t3grff vector,

  If the acceleration of an object is always directed perpendicular to its velocitc00k9 routy/j;zd, 6ez sx kfnq,1e,i9 y 60 eodkxq,iezn, kszc1f/rt;u,0j y,

  At what angle should a water-gun be aimed in order for the water to land with thm( kt j18*ugyoe greatest horizontal g( yom1t* k8jurange?

  An Olympic athlete thkp8dj )b7dxtm+g 6jc/rows a javelin at four different angles above the horizontal, gd+td7/jx68cjm )b pkeach with 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 secichrcyo0s k(m: 4 0)fkond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) woukmrc:(0 h iof yk4)0csld be

  A ball is thrown at an u y3t /5uxsbs/original speed of 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 sc/)yary cyw6a-z/ k; field goal attempt reaches its maximum height, how does its speed cwrc6k-as/ yy)z;ay/ compare to its initial speed?

  A stone is thrown horizozbbwl kh )u81b52vim)ntally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the leve)m1)vh buiz8lw kb52b l ground below?

  A bullet is fired horizontally, and at the same instant a secops 1v2 oj3aob8nd bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the twbo 1asjo 82pv3o bullets.

  A plane flying horizor47 :u+l0tjt31cdazgzllcfs g9 ww 20ntally at a speed of 76.0 m/s and at an elevation of 265 m drops a package. 3.4 seconds later it drops awglfcc u3l9t jr2l1a4wt00 z+z:dsg7 second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second 1yubpj0ay// epackage is dropped. Neglecting air ree a/b1up/ jy0ysistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spqsebh6 )d2wd xj6w /+:3jsqbfeed. Neglecting air resistance, when the bomb hits the ground the horizontal l/)sxq6de: jw3w6 2bqdsjf h+b ocation of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that o4lqil:dkovv6:.j 8z) p so4urn Earth. If you hit a baseball on the Moon with the same effort (a4 8v:) ljkdr.ui46ovzo : qsplnd 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 toj4; tm)pn+s+,xq fdea a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the om+j;ft)s+4n edxq,pa ther car is

  You are trying to cross a river that flows due hwp8b9twyk3v/. 9k 2off yu.qsouth with a strong current. You start out in your motorboat tp fo9/qwvh2.bu3 yyk8w9.f k on the east bank desiring 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. How much time will it tai /2e0dkdq/f hsuv;z 7ke you to mov d/e/isuhdqk2vz07 ;fe 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitudej-t)ne7 myyic z0l zrr9a2*te)dj- p; 8.0 m at an angle of 30 degrees below the +x axis. The yrl y)ye* 9djp ir z)eajz0nc7- tt;2m- component of A is

  If a ball is thrown g*48*l szow1nnqqx-bwith a velocity of 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 straight line in a directio k/g2mp h)1 )d kfr0gfgaa;tt2n north of east and you end up 2.0 km north )faagp0)d2; tg/ kt h1mfkrg2and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a s5i ckb*w)tfmmv 0-p-szx6 9fgpz3k (dpeed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The ak0dzxks v9-(ztf3 )cf 6mmp* g5wipb-ngle 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 ground. At ivp 3p)ek89s; pjn x3iwhat angle is the Sunv k e83 9xpi)ijp3np;s elevated above the horizon?

  Two vectors A and B have components (0, 1z1 iu 5jo*yk;t4 phv0h) and (-1, 3), respectively. What are ko1hzh0itpvju4* 5; ythe components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 5i 8:menp law(3), respectively. What is magnitude of the sum of these twopw 8ae( 5mnl:i vectors?

  Vector A = (1, 3). Vector B =v/xjtx*0qh6 etru r;k j (h;h4 (3, 0). Vector C = A + B . What is the magnitude oex0*htr h h t 6kj;jv/(q;urx4f C ?

  A car travels 20 km West,gmztt.hnt +8z, 9 1mxn then 20 km South. What is the magnitude of its displacem+nn8.m 9zzhm,t 1tgtxent?

  Three vectors, expressed in Car5d(- 2(kfj p5bcht o*i vk7dpxtesian 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 coordinates-rw)5w; ; ) dj iie(aojkszhx+, 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 is the mag;:fxv xud 3hd6nitude of vector :uddx 3xf ;6vhC = A - B ?

  A runner runs halfway around a )ri;m5ufxo:49kht( ok(v/ hu. bcegdcircular path of radius 10 m. What is the displacement of the jogger(c/v mb5oftogrx)h9 iu :.uh4dekk;( ?

  Two forces are acting on an obje n11dlgigcp( 1ct as shown in Fig. below. What is the magnitude o1pg1nc (ig1ldf the resultant force?

  Two forces are acting on an objecfe*9*m+g1h i i*89g e j3vi+fseodrq ot as shown in Fig. below. What is the direction of the ri j+e*s v i8o3efd *1r m99ef*ghoqig+esultant force?

  Vector A is 4.1 cm long qnlea1** 0mzs and points along the positive x axis. Vector B is 9.7 c q1smea**0z nlm long and points at $+44^{\circ}$ 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 lotoz+7 00oaen/woyy 8j 0epm 0lng and points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 25 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 initu y 3:1m8 ia5hq ajq4lmdz )jdcd)zj:7ial speed of 24 m/s from the edge of a cliff. A stoa hjd48 )z)m: uqj3mj5l qc7i:aydz1dp watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of b :gaca+az2b;h+ i8hn8 m/s, from a bridge. It falls 17 m to the water belowa:bzan ibg+h+;ah2 c8 . How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, rcbvb59 e)x7rh k,b0 ystrikes the ground after traveling ho9r rbyb0)7 5cbekvxh ,rizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes intn*leds6i98 t d,f ;pnio the jump with a speed of 12 m/s at an angle ofl68td,; ii s* ednn9pf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into p0:i:-qlhaif the jump with a speed of 13 m/s at an angle :iiphqfa-:0 l of $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an ini:y:/ vs j;pqjrtial velocity of 29.2 m/s at an angle of $26.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 45(/p92e+d wz-ve5f pqlwgtk8 3ude f.b.8 m/s at an angle of $19.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at 2yhv5j,-be dur05 ;nvc adh8qan 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 at bm8wt,zjb vq d:4sck(. p7mj3 24.5 $m/s$ from the roof of a building 50.8 $m$ 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 spe-kcf+a+h9m yw ed of 49.2 m/s at an angle hamw+c9+ -ky fof $46.3^{\circ}$ 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 mgmx2q n5z) cw4q c)e-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 tq5qgc)4x) men c -wz2mo finish would be

  A plane has an air speed of 200 m/s due North, and is va+rg .j;v-o ein a wind of 50.0 m/s to the West. The planee.g+ j-vov ra;'s speed relative to the ground is

  A plane is flying due South eu:0xalf +b e(mn3 .up.km 6cz($270^{\circ}$) 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 headeph)7zj(yt.ht d $30.0^{\circ}$ 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/p,(feufl, vfr1 vp3n whdap:mq*9c8u,z -ob m/s horizontally fires a projectile with speed 50.0 m/s in a forward direction pa uhec3:1-*b,o w8/nrfzfd pv 9v(mq f,up,l$30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed /rq h+te3yki3in still water is 8.0 m/s, is directed across a river with a current of 3h yrtk+qi3e/6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat t:bg* hm9.gl6j,t +pj c3bbqevhat can move at 11 m/s in still water wishes to travel directly across j.b tg36gv+:b p *jh,bq emlc9a river 1.8 km wide in which the current flows at 3.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in st 42bobrqi n4400krs:s gu4n deill water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should th4s 4 b n0q2:uk n44sier0dgorbe driver head the boat?

  A swimmer heading directly pio,eg-gdn 7::wx j;oacross a river 200 m wide reaches the opposite bank in 6 min 40njo-o7g:gx ;p w :ie,d s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reach(r7x/ nlz7 +xjeo i9h 8vq1bvhes the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of i7l /xvnvr(+e8q79b h1zhxojthe current?

  A boat, whose speed in still water isx r blirocd4o)fs1i0*+ e5* ym 2.18 m/s, must aim upstream at an angle ofm04 5eyr ic*lio )f1 or+ds*xb $20.3^{\circ}$ (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)  $m/s$