Which one of the follli (44/qz h)y- 4gk2fqqjgdpmowing is an example of a vector quantity?

  Which of the following oper.,6h vqer-jgrations will not change a vector?

  Which of the following is an a ze-vgcm7; g5tccurate statement?

  The resultant of two vectors is the smallestnlmt x-e v fvodksd.07 ry-789 when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 mu-ug bf 1eea*,h,*5tfio j xl*, respectively. When these two vectolu,f* atug e1f ijb- 5**eo,xhrs are added, the magnitude of the sum

  Two vectors, of magnitudes 20 andf l2swe6 6lfy7 50, are added. Which one of the following is a possible answel7y6 2sfe6 fwlr for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dir)oaw5 g v5gftyq*tt* 5 nxbu/.c vha:o *.9lojections th *yn.9attg5bq : *lxvw*av)uj5o5 fctg./ho oat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unku16ihvzen1 3rnown vector is

  Ignoring air resistance, the horizontal component of a projectile0bp;v;;rc tx3f lpin+ksv13llb- -fs 's velocity

  A ball is thrown with a veles0xfetp iwkv t 31d8i9 35o/wocity 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 projec7dvap w7b0ib+2 k wlw8 1nje(ctile's accelerationapb8 +w1iwl7 (2kd v0n j7ebwc

  A soccer ball is kicked with a velocity o. x2 bdrr-.ie1lt:7gmp 2yf/jqv1u ljw ;ahk ,f 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 vn/ia)yd 8/if dector of an object is directed anti-parallel to the velocityd8y /i an)/ifd vector,

  If the acceleration of aj1b *nwa1wpb4 rmt21: ikjo, sn object is always directed perpendicular to its velocity:i,mj1rob b24wpnj 1* 1s tawk,

  At what angle should a water jr9h+det xx5w,6kj:p-gun be aimed in order for the water to land with the greatest hor:+,p dxkxwj596 hejrtizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizon7m1 qpd v1o;8q,xulh xtal, each with the same speed:hq;lmu71 pqd 1xv, ox8 $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 tnywdvq) ) wmxn+0b cf64jcd1 ;he ball leaves your hand with twice the ve0q)dyfd 4x 1w c6mn;w v+b)ncjlocity 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 8.0 m/s at 5o ,+v lunw wmnxp1-j.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 reachedoej9 ,,tah x)29kd fjw/bl uxru;88b s its maximum height, how does its speed compare to its initi8detr9,ok;2 abub/dj xw ju 89fx)lh,al speed?

  A stone is thrown horizontally from the top of a tower (m/62 vhs04k pdezhp q- 8dncsat the same instant a ball is dropped vertically. Which object is traveling faster when it hits the leshp( 8cvn p-2dq40sm6dhk z e/vel ground below?

  A bullet is fired ho8vwm; w b ,y(,,wiccycrizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Comyc, ibwwym w;c(c,v,8 pare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 107.8 m/s and a1uexrepy x+ub n8,j0r n--e b,t an elevation of 258 m drops a packa , 0 euruepr-yb+jxe-8n1bnx ,ge. 2.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dro 5jjjk-4ave x4+/ibe . 7jnoe qfv,/ihpped from a plane, and one second later a second package is dropped. Neglecting air resistance, ,boj/ij 5e ji-en7jevv kfh/4xq4.a+ the distance between the falling packages will

  A pilot drops a bomb from a plane flying hori8ti+)rqly ez:wt5m e2zontally at a constant speed. Neglecting :ettl i)ew8m+2qyrz5air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixr+mrb1f+dcu 6doq si 37u /*juth of that on Earth. If you hit a baseball on the Moon with the sambu7im+d+uscrudrj*3fo 6/q1 e effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi6 3le*8 qqiyhs/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative vhqq3lsy i*86 eelocity of your car to the other car is

  You are trying to cross a river that f+,jij ytmxzpj. k ,g2w0zpz4 2rfn63w lows due south with a strong current. You start fwtz py,2g.2 n x j zmk4wr60j,3+jpziout in your motorboat 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 tim gv-ryi t+v)5je will it take you to move 12 km - r5tyg iv)vj+downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at a-fwwp j2 +mv6oa9/mrk.ni,xv/g k8lhn angle of 30 degrees below the +x axis. The y component of A iw m6kvflra nhg/o .x/vjpik2+m ,-89w s

  If a ball is thrown with a velocity of 25 90rdpx.eq1 5t ilrt it 8,(lhlsfp68hm/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 3xe9c --0lmbjdgu+b cin a direction north of east and you end up 2.0 km north and several kilometers ea -9dbc3l0c+x ubgej- mst. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of it u2-v a7grj*1xf k- bi.c8s+s und9pzykem)4bs velocity is 8.00 m/s. The angle between the direction of its motion and -4 9ekd. bcjsr8ixyz -muv)2 bas* +fgpnu 71kthe x axis must be

  A 400-m tall tower casts a 600-m long shadqopz7xqt ib+ jpy71+ /ow over a level ground. At what angle is the Sun p/ +ijqb yt7oqp+17x zelevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, wi ,7 luuq/:x- oed x5n+jg82,omdacbyl)4sk3), respectively. What are the components of the sum oyul/w)+iold: es 48j, qca bkm2 5xn,d7xgo u-f these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatdwr1d6p22 8yby gr*ye is magnitude yb w2g8rdy r dy26*pe1of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A 4y/c6 abici4u + B . What is the magnitude oi 4/cyu 6ic4baf C ?

  A car travels 20 km West, then 20 km South. What is the magnits eyo-7qs6 2g w4fvrsi3 not-+ude of its displacemen6qivo-gs4nw2 y+e37r sftso-t?

  Three vectors, expressed le+oy4vfc8th ie5 z32 in Cartesian 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, expresse2n u +*p jvcx5ft35x5todb:u + a7tfimd in Cartesian 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) a6bf9wzd0 vp12 6zfjsmegg7o 0nd vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B gzweg m29ffp6610v0zjsb d7o?

  A runner runs halfway around a circular path of r1kfjm:9wzg 2:qcu1oj2. v kk 0imqo f5adius 10 m. What is the displacement of the .:oo0mvff2 q u21ckg5 kk:qjizm 91wjjogger?

  Two forces are acting on an x- zjd5j g-a4b9,kwbby e.kg:object as shown in Fig. below. What is the magnitude of the resultantzyd.w xa,4be -kg b 95b-:kgjj force?

  Two forces are acting on an object as shown in Fig. below. What is the directiofft.1ovjtagt- gfe6 0+f3i uqn5 rv*.-5gc aqn of the res af.u 5tf.q0 t*enqo3grj gt+cf6 i-v1fg5a -vultant force?

  Vector A is 3.5 cm long and points along the positive x ax*lth 830z m5okn9 -n, qy*suugo6wfgjis. Vector B is 7.4 cm w95uo k gsnfh*q6tol, y-3g *um zn08jlong and points at $+43^{\circ}$ 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 67 cm long and prk20p4f07iutcsoh ot+ l44 wgoints at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 38 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 14 m/s from the edge w8q1dwn-ihh;8 j s fx*of a cliff. A stop watch measures the stone'h w1hn-8fj ;dq wxi8*ss trajectory time from the top of the cliff to the bottom to be 3.1 s. What is the height of the cliff?

  A girl throws a rock horizontall8 h aa b7f3aarv+d.5htd 6;pipy, with a velocity of 9 m/s, from a bridge. It falls 11 m to the water below. How far does the rock travel horizondpfh8r 7h ;pib6aa5 3tad+.avtally before striking the water?

  A ball thrown horizontally from a point 20 m above t8q1ip4 kan7 thsh+mvnq kl ,-+he ground, strikes the ground after traveling horizontally a distance of 15 m. With what speed was it tkh7hati8++ 4vql1m,ps -kqn nhrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/scj 3w m;f+enj+ c)buc6*mr(u v at an angle cu bf*erm3j c +jc6w(+vn)m ;uof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-(s8;7* clueevhq a2:fm hns ;tjump goes into the jump with a speed of 14 m/s at an angle a: s*lhhnsm2;f8;veetq(cu 7of $26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 52.5 m/s at an ang*1lmr1nq c0kqte y73t1 mpc( ule of $38.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initiamj h336kmiajp0((rmkzzd t4:z ) g6erl velocity of 51.6 m/s at an angle of $24.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired aykvlvl *7g,0zh m av24t 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 at 19.8f qbr.c7riy*)+k wq1:ix /n lr $m/s$ from the roof of a building 53.7 $m$ 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 e85yq)8 :ty7cuwyyr: bizbu +55.7 m/s at an ang:yu zt+5i8 7cy:8q eyywubr) ble of $37.8^{\circ}$ 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.oqsyp0wj/3n9g- imj3(we 8zg If you ran the same 39-gyj og3 wzmj08sw(qi/neprace 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.l9 c5is cx9m te9wupj*ne(b8 is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground is( eci 99p8bwm jte5ulncs9.*x

  A plane is flying due South (h l5b ep:34bno$270^{\circ}$) 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 sp ,vik6jlv s;* d-7kkaveed 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 )qkiala.,l tlo6 2+ boa projectile with speed 50.0 m/s i ),.lt+o2a6l o alkqbin 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 directed across a river withh:rel1(m : fm+ vt-xxl a current of 6.0 m/s. What is the speed of the boat (:lxmm-+:ehxf1 l vtras it crosses the river?

  The driver of a motorboat that can move at 15 m/s in still water wishes to t1,-5 f2chqz ddthlok /08y9ge5px uuu ravel directly across a river 1.7 km wide in whiczd gul y1/utd,- f525oh8uqkp9 chx0 eh the current flows at 6.8 m/s. How long will it take to cross the river?

  The driver of a motorboatax tk/z,xx48 g that 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 h/k8xx 4a ,xzgtead the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite ban*6q dlx3k,i,azdm nike(ka/)mql45w k in 6 min 40 s. She is swept do4*kwld mkiin q,xa/d(,l 6zm5aqke )3wnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank ybri5h0sdqw 2 )jc)x2in 6 min 40 s. She is swept downstrxi)0r 22dj hqy 5c)sbweam 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.80 m/s, must aim upstream at an angle o5; jq+to skay.f aj yt+ks q5;o.$23.2^{\circ}$ (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)  $m/s$