Which one of the following i vecsz5mn .*o6s an example of a vector quantity?

  Which of the following opej038e)c iez 0qah9mkhrations will not change a vector?

  Which of the following is an accurate statki -:1w c7 ahoc93dceav3uii9ement?

  The resultant of two vectors is the smallest when the angle between thqtyphszm35o7w- gcckq lm44i2 , 5gz8 em is

  Two displacement vectors have magnitudes of tb1vd23++d9atwqp:l. m oxe e5.0 m and 7.0 m, respectively. When the +pvltw93+ exmtd 2aq:1bde. ose two vectors are added, the magnitude of the sum

  Two vectors, of magnit0r1 fv 4fpol8vudes 20 and 50, are added. Which one of the following is a possible answer for tfrp4 8o0l fv1vhe magnitude of the resultant?

  Three forces, each having a magnitude of 30 N,:mazm46z b( bv:w 1uvk pull on an object in directions thau6::mkm4zv bzb vw1(at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector isvy9v3yuu (hhc4qq /v7

  Ignoring air resistanc00-d60s bunltt x3ztye, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of))kzt2pd q98izfl h*wxpc2 , u $60^{\circ}$ 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 proje5*,qx /7aqhrh6r n ywlctile's accelerationw6/7*rql yh5 haxq, nr

  A soccer ball is kicked with a velocity of 25 m/s at an a*;d al(;nxnp29szab2 u/jn ou0chr g3 ngle 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-parallel to the velov+ve)tnc2o1 s ly.t ycma835xcity ts nl8 . tym2x+cao13) yv5cvevector,

  If the acceleration of an object i1tp5b ggo4mud uuvp, i z399r;s always directed perpendicular to its velocitg9t v9bp u zd, i;uguo4p1m3r5y,

  At what angle should a water-gun be aimed in order for the water to land j (b0f:igd0 os 1xds chx2)rmgf8wj3(with the greatesthx(i 0j0cmsbx gsfj)odg2f(r 38d1 w: horizontal range?

  An Olympic athlete throws a javelin at foupd-19k)c yaqu yv33 rsi7 o/tir different angles above the horizontal, q7 s/tyac dopyi 3iu 9rv13)k-each 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 second time. If the ball leaves your hanrt;0 i:).qa 5kya dksbd with twice the velocity it had on your first throw, its horizontal ski)y qt 5kbda :0.a;rrange R (compared to your first serve) would be

  A ball is thrown at an original spetdo:d9w3 m v*oz4/ hxted 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 field goal attempt rea4/tknr zy;ro2gd 0k5;/c z rjyches its maximum height, how does its speed compare rzyr4t;/ojn/y 520d kgzrck;to its initial speed?

  A stone is thrown horizontally from the top of a tower at the suo,e7.n phy( vame instant a ball is dropped vertically. vu nyh.7(pe,o Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a slv c2lh i/0m az6fc(e6econd bullet is dropped from ta2c0i /hvm cl f6(e6lzhe same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a sq;bw*e suj1gcm*,+b3a/bg, sub bf2 wpeed of 46.9 m/s and at an elevation of 131 m dru2faubm3;eb ,w*s,gb1/ j*qg sbc +bwops a package. 3.3 seconds later it drops a 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 bm3 aqsz yq(cq 77d4c18p/ xgppackage is dropped. Negl7bzg4q37qp da/ 8y(x 1pcsmqcecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spe0 ,yk/s pho0-n cz,kugnsu2:m ed. Neglecting air :gk0z0msnn y,/2 puh- su, okcresistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixthg+13 fyggdy:w of that on Earth. If you hit a baseball on the Moon 1g gwf3:yg+y dwith 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 g/4 ognt 3;1/ mn+hddg8toxhm+x axis relative to a straight, level road and pass a car traveling a1gt o/m+h;n3 g /ndom4hxt8gd t 45 mi/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 strong current. Yjjq0/4h plm i4ou start out in your motorboat on the east mjhp0jl/4q4i 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 tirhl uv w3 atu-+9/qnv4me will it take you to move 12 km downstre +9vnhw u l4uaq/-vt3ram, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thc+6f.q(7-x c:y vn5 jxmtet ige +x axis. The y component of A ix n7+x6cvgmj5.-tc(qite f: ys

  If a ball is thrown with a velocity of 25 m/s at an angle of .;2*92i-f gvb vzmv b+ts qrwmb)s4t j$37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direction northl6+ +m n wqvdq5ickr 03)g;uci)teq 6i of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have youm+ ivw)d3) q 6 u;0r qkc65igln+ctqie walked?

  A butterfly moves wiajjvp +8d8q-bufpg ((th a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its mj vja8 +-pdub pqfg((8otion and the x axis must be

  A 400-m tall tower ce+e ;+qji r*20i w6 yoarii2eaasts a 600-m long shadow over a level ground. At what angle is the Sun i aj2ee warioiy+06r*;eq+i2elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respejg5iwlfg4 keqe(d0n: ou128xvc r(c7ctively. What are the components of the sum of thesxv2ue :5kr (idc c j wneg(7lg8qf4o10e two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wh(i ;y5ik hza a.6j7 ;w*udrmc)ylsr3qat is magnitude o);.yh5z ;cmr3qsw7 6 kdrjuay (la* iif the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = d1.by 9c8xgtx A + B . What is the magnitude of8tg9 cxx.y1bd C ?

  A car travels 20 km West, then 20 km Soul*ue0 juzgzv3.7;wjz th. What is the magnitude of its displac0 .7wu3 ; lvjzujzg*zeement?

  Three vectors, expressed in Cartesian coordinates, lklx.7 l/h.p4r qp:ftare
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 coordinatjp :ap)r)bj/ les, 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), syt)+g8 ump -xe7j,(o c-;cktvnsh1z what is the magnitude of-pt uejc kszhgv, tmy1) (+8 so7cx;-n vector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is tmtk9 .0bg pej;he displacmjte k9. b0g;pement of the jogger?

  Two forces are acting on avw9wg w),ra5pzk*m *) ue1dcan object as shown in Fig. below. What is the magnitudekregmvwazw )wp *)5,c 9a1du * of the resultant force?

  Two forces are acting on an object as shown in i) i9rb9fs yoe;g ol/3Fig. below. What is the direction of the resuyig /o9seil9;)bof 3rltant force?

  Vector A is 3.7 cm long and points along the positive x axis. Vectoa2 nvr,-mp, brj sp0-xr B is 7.5 cm long and poip2,r x- navm rjsp0,-bnts at $+33^{\circ}$ 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 79 cm long and points at2,k bltubfk 75 $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 49 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 23 m/s fromlmcz ynm- o101 the edge of a cliff.m 1oc0ymz-nl1 A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.0 s. What is the height of the cliff?

  A girl throws a rock horizontalllk831n1sf)sk ru qf8ay, with a velocity of 11 m/s, from a bridge. It falls 27 m to tsl8k8ku f1fr1a nqs3)he water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 19 m v bnqg1gjf-9iu06;bh above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it h -;fvb196ub gng0ij qthrown?

  A jumper in the long-jump goes into the jump w5ayer ) pu)zcdkya7:f-u z9 ,dith a speed of 12 m/s at an angle of u )fc5a:7a -pyzz9y)dder,uk $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long- d,5nznl-ui/ubd2 25uqwl m-qjump goes into the jump with a speed of 9 m/s at an angle o2- ,uzd-bid /qmn lu25wnuq5 lf $24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 34.8 m/s at gu03lh;f+8 rju qemi0an angle of $23.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 25.0 m/s at an angle of j ;p7zswf;k-xuh, g 0u$26.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired aw) p,,kgj:f+6 hn hx-ct)qupz t 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 hom, z6ltb 7;qadrizontally at 25.4 $m/s$ from the roof of a building 62.5 $m$ 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 friex.j m4eb )t.om ground level with an initial speed of 42.1 m/s at an a bm)..e4 jextingle of $41.4^{\circ}$ 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), ro8/ ibe38 o6b3p3r4z wulwxayou can run 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 conro 6zwou83pal34 /ebi3b w8rxstant 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 7/sttidkb .g 4hadp21tf*ya/of 50.0 m/s to the West. The plane's speed47dpi/a1 aft/ b*htgtdsky2. relative to the ground is

  A plane is flying due Ssm6d,jc;1 ( (.dgohxalf z7 wtouth ($270^{\circ}$) 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 spee wwd:: e)btc+qm+g-kzd of 120 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 projectile with speed 50.h;srr kt ac /mzarzb2x :(h -q-mu9-6 otm/mq70 m/s in a forward dtmz-(7:hsmr/trouq -a2rm6zm9a / -c;khqbxirection $30.0^{\circ}$ 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, b4mn30i obj ud8max(: is directed across a river with a current of 6.0 m/s. What i(x4d08noa:bm3 m jbu is the speed of the boat as it crosses the river?

  The driver of a motorboat that can mov8wdd:er tilq8;uzc+a la( -,d e at 15 m/s in still water wishes to travel directlyd 8+c;q-war:dezu dit (,lla8 across a river 0.7 km wide in which the current flows at 6.3 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 wishe3jr cu 4jl6u6bs to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driverj r6u4b 6ucl3j head the boat?

  A swimmer heading directly across a river 200 m wide reaches the op;l aom.)e+ mrpposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still .oa;r+melpm)water?

  A swimmer heading directly across a river 200 m wide reac r:u/ w8+k/vrj (mmlfqhes the opposite bank in 6 min 40 s. She is swept downstream 4m/lr m: rkq(+jvuf8w/80 m. What is the speed of the current?

  A boat, whose speed in still9a6qo iwayg i x8o7s18ry7z 3l water is 2.20 m/s, must aim upstream at an angle ofs o16q8g7yi9 8oal7yaw3 rzx i $30.1^{\circ}$ (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)  $m/s$