Which one of the following5t 0fiyg+y/ell8 c9 rvy- 1adq is an example of a vector quantity?

  Which of the following operations will-t h cod9gy rb9.raxme5 /+.xq not change a vector?

  Which of the following is an 9:wza l-.jrbw) azh9saccurate statement?

  The resultant of two vectors is the smallest 7 v1d37s qv2f;eadptuwhen the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 mwnyb9 1xzl 2e5, respectively. When these two 2 zyweb95l1 nxvectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20xho9 zqv tl:bsn(k+g4 *,g +sn and 50, are added. Which one of the following is a posoz: b*nthgs+k,sn4l v+(gx9 q sible answer for the magnitude of the resultant?

  Three forces, each having aq+ ,l06*rbr 3rc a(p6wvl zt/iapj+ ol magnitude of 30 N, pull on an object in directions that a pp+(0boqi cr3zta + al6wljr*,6lv/ rre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoo;he1n5b( yt9(psp x xwn vector is

  Ignoring air resistance, the horizo (n(-3,:q 1obeq5lnavib xcuuntal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of t q):cvvj6o,mfd /8;jmmejdej5 -a8s $60^{\circ}$ 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 projectmd/f0n; vb6/77vqp obxiai *aile's acceleration60avadpf/ i;o qbm7i*7bnvx /

  A soccer ball is kicked with a velocity of :2nua05ms:tx(wt hc 2dz;ijk 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 directehd.)ch.mbq g*d anti-parallel to the velocity vectmh*q)chdb ..gor,

  If the acceleration of an object iknq-es60w)a fn-a n )bs always directed perpendicular to its velocity -)s nnb0kqa-fnw)e6a,

  At what angle should a water-gun be aime *1j (,ppolyyid in order for the water to land with the grel, p (yj1pio*yatest horizontal range?

  An Olympic athlete throwm21-cce8fl)lcoe zgb -o8 /jf s a javelin at four different angles above the horizontal, each) mfl8bcg 2lj/fcc e8z- 1oo-e 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 ti, +futm dzge10me. If the ball leaves your hand with twice the vel1m0 z,+tfu egdocity 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 oks)jkrrm) + /kf 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 reaches its maximum heigj iyu)m*oy/z.7*c 6x6xik upq ht, how does its speed compare to its initial speeoj*i/uypc 7) u.xm*y 6xkz6qid?

  A stone is thrown horizontallytp s-(eqz.dg + from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hitsesq.pzd(-g t+ the level ground below?

  A bullet is fired horizontally, and at the same instant as.fj c(p (;-mxlcndqpb s,/u(g r5 pv+ second bullet is dropped from the same height. Ignore air resistanc(.m(v5lbqp-ssg +pdrp/c(,jc;f nx ue. Compare the times of fall of the two bullets.

  A plane flying horizont:mi( jkc3:e ghally at a speed of 58.7 m/s and at an elevation of 239 m drops a package. 3.1 seconds later it drops a second package. ce :kmhg(3i j: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 pacnr *fihd d456(by1/ho qw wca0kage is dropped. Negle( wy6d q5h odfcwn0/bi1* r4hacting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horiz crr; .yy6akr;*gvtdf1r5p5 w ontally at a constant speed. Neglecting air resistance, when the bomb hits the grouna;ryr kv6yf cwdtg15p *r.r;5 d the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of .-s.q*/9 xg d,kpjx jya ;5mxuspg6gvthat on Earth. If you hit a basebal g/p;m xjd -9,uj 6x.as.pggsxqk5yv*l on the Moon with 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 +xtv1j7s :k9 5gqb3domt axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocityjt7mgd tv9b:qk1os5 3 of your car to the other car is

  You are trying to croo (mxsl7jv21ey :sib7m9j y f*;ww2tyss a river that flows due south with a strong current. You start 72lmsxvws j 7yebi *y 9;fw(t1my2:joout 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 cfyl62;ci(j8he f e3tkm/h in still water. How much time will it take you to move 12 km downstream,h(8 3lcey fje f;ci26t in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belj +2d9oy.bs4qyiqm i 5r2 xa3bow the +x axis. The y component of d4x+2i 3by mjo2si9aq 5q.byrA is

  If a ball is thrown with a velocity of 25 ov aeswubl)/0si+ 8-s 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 stra;lecvkze 0pv o3,rcap/62. ka ight line in a direction north of east and you end up 2.0 km north pvzk30,o/ k 2ae;v.ec6cralp and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed on1ur0.4(msks aakx8s g6 qqy *f 12.0 m/s. The x component of its velocity is 8.0 ( ssq uaq*ykk164nar0g m8sx.0 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long aw f06 wsz*y*bshadow over a level ground. At what angle is the Sun ebyfwsa*6 *w z0levated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), r33 zv2r8ing*y. 4svfmvfo(gaespectively. What are ton2ig g8r 334vs*a.my zf(fvvhe components of the sum of these two vectors?

  Two vectors A and B have components 6v+xt srtdj6p1 9l,tv 8 vy0gk(0, 1) and (-1, 3), respectively. What is magnitude of the sum of d6gpj0v9 rtt8 sl1,v+vxt6yk these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B .,dwf* / *13dsgtcls pb What is the magnitude of C ?fbw,sd *gt1c*3l sd/ p

  A car travels 20 km West, then 20 km South. What is the26xy. jumvmny 6qr0l),zoi3 o magnitude of its displacemim2qy0on 6.vmo6x,j y3u)zrlent?

  Three vectors, expressed in Cartesilh0n 37)q2o 4delobiuan 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 coord:+;8xgh19rqc mp/ l r9pqkyyo inates, 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, j//7v4jfegw8ibo e3g -8.0), what is the magnitude of /ev gje ib837gwo fj4/vector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dis0wlnfg0cg4 m4w4zclebl. 0 6 vplac.4vzegcb4l 6m4f00w0 g cwllnement of the jogger?

  Two forces are acting on an object as shown in oya5()v6(ss niz qgj7 Fig. below. What is the magnitude of the resultant 6(vnisyq j()s7a5 zogforce?

  Two forces are acting on an object as shown in Fig. below. What is the directi/(cyzz( : xt,p m2jz2srs/rd son os/zz( rm/pxtcy:s( zr ,22dsjf the resultant force?

  Vector A is 3.3 cm long and points along the poj4f+ljk4v rkk0 . z61 ,npmqsrsitive x axis. Vector B is 8.8 cm long and.f6n 1rj,k k4jpz+4mksvr ql0 points at $+26^{\circ}$ 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 73 cm long and poempwti+p65t 1ints at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 44 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(;+uvap pug;z with an initial speed of 15 m/s from the edge of a cliff. A stop watch(pg;uv uz +pa; measures the stone's trajectory time from the top of the cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, wik b aw5h1wd,5xth a velocity of 9 m/s, from a bridge. It falls 14 m to the water below. How far does the rock travel horizontally before striking the water? bw,dxwa51kh5

  A ball thrown horizontally from a point 26 m above the ground3/ vcbnc) mb-t, strikes the ground after traveling horizontally a distance of 15 m. With what speedn-/cmbb 3tv )c was it thrown?

  A jumper in the long-p-.in3v y +2 yczlrq0tjump goes into the jump with a speed of 12 m/s at an angle o l0+cr tzyiqp2yv.3n-f $20^{\circ}$ 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+k;mu zw sjr::* yhd+b with a speed of 10 m/s at an angle + hjz:* ubmsrd:;wk+y of $25^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an init cy3 x z,)g 5glsdec(qg91fq-nial velocity of 35.5 m/s at an angle of $38.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initi 1pxvt..elp b:tpvv/ 68qt(ff al velocity of 33.4 m/s at an angle of $36.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of ia b1.v,xg6 tzldn1i,$30^{\circ}$ 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 hori8uwafrx; )- -n,4x-ssveefjxzontally at 24.5 $m/s$ from the roof of a building 31.6 $m$ 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 level6ln+i- )wc5e 4i q+bal qy+lgl with an initial speed of 39.1 m/s at an aqla w4n+leb +5y+cl l- igq6)ingle of $43.2^{\circ}$ 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. Ifs, oyv7(g jtfs +yg6x1 you ran the same race on a day when you had a constant headwind which slot6 s+,g jyfv7(ogxsy 1ws 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 Nov91o cd)batxab. u -2orth, and is in a wind of 50.0 m/s to the )odtcvo 2u x91ba.ab- West. The plane's speed relative to the ground is

  A plane is flying due South (ck;e37nl 51ra6 eb ori$270^{\circ}$) 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 -ayd1 , fywvp-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 50u0qc)e,i p z(j.0 m/s in a forwardz)q ,pice 0uj( 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 riz s8ls5-w rqh15a4pjever with a current of 6.0 m/s. What is the speed of the boat as it cros-rh4 ps zl51q85saw ejses the river?

  The driver of a motorboat that can move at 10 m/s in still water wi- ayk0v:57kws x5 s-rttlw az-shes to travel directly across a riveswt r l-a v5xt-wy:-zkk7 0a5sr 1.8 km wide in which the current flows at 6.0 m/s. How long will it take to cross the river?

  The driver of a motorboat thate()4tkwo1;j,fpjz +) ydk v,ua,x jiz 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 upsd1i exwyf)z+j, ,(o; j4au tp,k zjkv)tream should the driver head the boat?

  A swimmer heading directly across a 6 x-m 7zo55znerfctq3river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast 5r3-o6zfxnzcte m57q can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bankpc0gaz/k )300gbgzqg. m dw8p in 6 min 40 s.gg/.0a0wgz p3gk0 qmcbd8z)p She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is vm4f- t c0l gy( 2ktvdd6h5d6b1.48 m/s, must aim upstream at an angle of5f06d (ylmd ck vdbgv-tht4 26 $15.1^{\circ}$ (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)  $m/s$