Which one of the following is an exampc dbz9.a: k4zale of a vector quantity?

  Which of the following operations will not c-qxm(dg9) c pmhange a vector?

  Which of the following is an bge:oyrm m4-2accurate statement?

  The resultant of two vectors is t) ,z:zc5j fc- k/zun3j;awjhnhe smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 r qb0 /sb3 ( ,ijwqzrvcd*.ks+m, respectively. When these two ve(sbsr.v d qjr+kz,i 3 0c/w*bqctors are added, the magnitude of the sum

  Two vectors, of magnitude oajfi7mn*,25u u y.rfs 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultant?j*uoun 7arf.,m iy 5f2

  Three forces, each having a magnitude of 30 N, pull on an obfgb+:bs0:ss ejltb;; ject in directions tha+j;l gs ;febb:tbs0s: t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector5kaz yq;c -7b4bt ll*o is

  Ignoring air resistance, the horizontal component of a projectilensi* dz;p .lpg2/lgq7's velocity

  A ball is thrown with a velocity of 20 gw;m7gtcrtxzn3adwi ot o 3kw;*2:g,-l5 s7lm/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 projectf3f;)c;t xhn xile's accelerationn)3t;h fxfc;x

  A soccer ball is kicked with a velocity of 25 m/s at an angledn( 8()zgg(.gwp * oswnk7jc i 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-paralle)zzum *q/bg lul4u:wn9/l ,gol to the velocity/n mo)/l g4zq ,bu*lul g9:zuw vector,

  If the acceleration of an obnr z0wq.)ez 6lject is always directed perpendicular to its velocit wn.0z6)le qrzy,

  At what angle should a water-gun be aimed in order for the water to land with thv4o/lphcj- wdy 43 lm4e greatestwhlp-3 /jmv4cd 4yl4o horizontal range?

  An Olympic athlete throws a javm ttww*o3*r bbcncl o51(hz (+elin at four different angles above the horizontal, each bohcot5cr*w( * n3zt( 1w+blmwith 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 dp90. (ttr zs3jyr6wf leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve)30p.d(rsfj wr69tzt y would be

  A ball is thrown at an original speed of 8.0 2 27rxy6 llkcy)dht 0bm/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 hei*v2n rlcx5c4tgk(* qught, how does its spelcngv4 ukx 5qt (**rc2ed compare to its initial speed?

  A stone is thrown horizontally from the top of a tow9p4e llztvzl+gvd2/ia5/qo3 er at the same instant a ball is dropped vertically. Which objecvvl+2 5 p/ge4azlzl/ t3d i9qot is traveling faster when it hits the level ground below?

  A bullet is fired horizontally,letbm3+h8b i7-qda (g1rj3q l and at the same instant a second bullet is dropped from the same height3 mgj( 8+b hq 1ielalrb-t7qd3. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 87.we wq 3a2y0i) rkh1/fy3 m/s and at an elevation of 296 m drops a package. 6.9 seconds later it drops a second package. How e) 2hqyy /f0k3ir1awwfar apart will the two packages land on the ground?

  A package of supplies is drop x+l1kvr rt .itj ck+ yb:ao7/ln*zr l45t+ct1ped from a plane, and one second later a second package is dropped. Neglecting air resistance, the dista4 bv+tlkt1ntz+r:l75j ry il t .+*oacrckx/ 1nce between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Nen).; rckd-y yeglecting air resistance, when rd) ;yc.knye-the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity:8ia- /zl6q9nsita(pic a yi, on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would l9ti :6 s ilpaya-z(nq i/ic,8aand

  You are traveling at 5u9uq m89 roivwn8s: 5g5 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 miqi9ogmu s88w59:rnu v/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 curoihq 9zsdj j1+s7))g9f+yrlj rent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You sh+fsjyhlzj71o9 ))s d +9qirg jould head your motorboat

  Your motorboat can move at 30 km/h in still water. How much tip..ej an icc: 9 gemj(-xa2tr-me will it take you to move 12 km downstreajag - . ti-arpnecc:(ej.m9x2 m, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angl atblc ;u6s:c6e mo;jpncxke-+b6 3j,d7,rjy e of 30 degrees below the +x axis. The y compon+ak6,st;cle,p bj c:cdj 36xn emur;7o-6y bjent of A is

  If a ball is thrown with a velocity of 25 m/v 5qk2t5+mw -lbnj6rns 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*1 yipo9yk. eg a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have yy p.kg1y9oe i*ou walked?

  A butterfly moves witm)xd ehs, j 1q lq fohw1qi7x,xk68*4zh a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. Tx8i1h*w61 q4xq)sq d jk 7xfo,,elhmzhe angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadvdo, fb n2;qc lkis2qw3) g+f-ow over a level ground. At what angle isfnos+ l2iq)g dqw2b fk c,;3-v the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respe9iz0di :*rpzt 3.drwl ctively. What are the components of the sum of these two dlr0r3w zi *9.d:tpzi vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wha vnd91 vv,2g5jvm2vua t is magnitude of the s,1jg5 mvdvu 92vvan2v um of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C =gn:, +86bo32tlq 1tn .wdepag 9ah+werc in f( A + B . What is the magnitude of C 1bhwp6c 2+ oialwa(nq,dt9nng8r fte3e g . :+?

  A car travels 20 km West, then 20 km South. What is the magnitudey xnns :wvhxoj2; 71,y+ha s)v of its displacsy;7ysnao:2vjh,x 1hx +v wn) ement?

  Three vectors, expressed in Car 5a7lh p g((bsyw 11gco6w;cd +w:acdztesian 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 i pvn dj.m lfjiqef7y3c*.-e.2n 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) and vecto6x )b5ynsdb9ar B = (+3.0, -8.0), what is the magnitude of vector C = 95babsnx d6)y A - B ?

  A runner runs halfway around a circular path of radius 10 m.iqldt()w; x*htj.ra 1 What is the displacement of the jolr . t) *dhi;j(aw1xtqgger?

  Two forces are acting on an object as shown in Fig. below. What is the magniy:)qemxgr.t)6 m (cek tude of the resultant forcgqemk ).) 6xet:cy (mre?

  Two forces are acting on an obepvybt xk) )mh .lana6r/ 6(0tject as shown in Fig. below. What is the direction of the re h.rkn taybm0 le ()ap)6xv6t/sultant force?

  Vector A is 4.7 cm long and points h,8: 7fd(hkmvz pndv. along the positive x axis. Vector B is 9.9 cm long and points .ndfv h,(pkvh7: d8zm at $+55^{\circ}$ 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 61 cm long and point;l(lmevhc 3 5ts at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 45 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 wi ieo-;l(3 *wp- s+j5xr*w-mcx wqniicth an initial speed of 12 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.5 s. What i(s* mi-li-c3ow wc ri;x*5qjn +-pwexs the height of the cliff?

  A girl throws a rock horiz z,ei/s.siy9v ontally, with a velocity of 9 m/s, from a bridge. It falls 18 m to the water below. How far does the rock travel horizontally bef.i/v zi 9s,seyore striking the water?

  A ball thrown horizontally from a point 24 m above the grounxz0-z tafp1u1d9f p8.r )wngnd, strikes the ground aftenu0 a rp1z-gpd91z.f8ft nwx) r traveling horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes inte0 5mf5bpf b2aeh3vahy.x.6c o the jump with a speed of 12 m/s at an angle of va 560efpm 5h h.ef.2a byc3bx$20^{\circ}$ 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 speed o v01 +eue-h frxpktt03f 13 m/s at an angle eh0tt3p +rvux0k-1f e of $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity oxpx i9u ;fgb-.a66kl wf 58.2 m/s at an angle of $36.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 48.2 m/s at an angocd 7rr;c-c8 zle of $24.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ol 1j)ya24ko id7ctk /df $30^{\circ}$ 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 horizontally8gelfy (yn25d at 16.2 $m/s$ from the roof of a building 57.6 $m$ 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 grz tr-vmgj7 ,5m6v hk)yound level with an initial speed of 44.5 m/s at an angle o ,h5tjrm6ygz-7m)vvkf $47.3^{\circ}$ 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), yo5j ,dgnf kvy1n jz8z31u 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 constant headwind which slows your speed by 2.0 m/s, the time it would take you to fkdg581vn1fy,z3 nj jz inish would be

  A plane has an air speed of 200 m/s due North, an- fsiu. +vh+aod is in a wind of 50.0 m/s to the West.i+of +u.vas h- The plane's speed relative to the ground is

  A plane is flying due 4g/ax9igsb2lb t *t 3oSouth ($270^{\circ}$) 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 120sz.beul6q(( m y(5l 3hajbo 5w 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 projecgms3r4ft 7+o7h *frjap4g5 uxtile with speed 50.0 m/s in a f ph+ *4 jf 7mxt54oarsufg3g7rorward 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 wat0v-j pbk/0 jo-gp-f0e z;sj cw zqqy560 js5mqer is 8.0 m/s, is directed across a river with a current of 6.0 m/s. W5sqj0pg00z6ve cfqb w-0osjjy kp;/z -m5q- jhat is the speed of the boat as it crosses the river?

  The driver of a motorb pt4 mrex05-rqoat that can move at 10 m/s in still water wishes to travel directly across a river 0.9 km wide in which the current flows at 3.5 m/s. Howem0r5pqx 4 t-r long will it take to cross the river?

  The driver of a motorb0ywhu9f7 h*nasn8m)ic 7wy 6koat 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/s7i67 myhcfu h9wn)*nya sk8w0. At what angle upstream should the driver head the boat?

  A swimmer heading directly across / :kmpstse1t1 yl2f c(a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstret:ps fcly1/skt2e m( 1am 480 m. How fast can she swim in still water?

  A swimmer heading directly across a :cbtf ge1 ck exq5*t2n(,cta4river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. Whatk5tx gne:qa*bft t,214c ec(c is the speed of the current?

  A boat, whose speed in still water is oe7.fg7m7u4c xj2 xd b2.06 m/s, must aim upstream at an angle off7xxog .uc4e2 jdb77 m $24.3^{\circ}$ (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)  $m/s$