Which one of the following is an q/9upxc 1fu3uexample of a vector quantity?

  Which of the following operations wi.b rvrr26502uqx cg oill not change a vector?

  Which of the following is an accurate sys)2km 5q1i;cc )mkrftatement?

  The resultant of two vectors is the smallest whenfz(w:o):j k /p(gtu ew the angle between them is

  Two displacement vectors have magnitudes yx0* r1qx4wl4rlx5y y of 5.0 m and 7.0 m, respectively. When these two vectors areylw xy*r y4 4xx0ql15r added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followt g;h 6*sp1-1grwi svving is a possible answer for* i;rsvg-1st1hp6wv g the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions ,4 pn3 gsmvy.q3pk29oz+rqtdthat am oppv2n3qdy. rg39qt s,k4z+re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkno zzs0z 5((dlkiwn vector is

  Ignoring air resistance, q4wa0 qda/ my2the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 2;sc+ fh:ky/ ji0 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 horizo29o-hfkxxp)l q,5gbv 9vhof r1(6aq fntal component of a projectile's acceleration(h kaq bog5h1q-9plff 2xo),9vr6v xf

  A soccer ball is kickedbo ;z0ue tok3d5z31f i with a 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 vecw7e(p68e cw- )ppjm *hvp) xio/ i.kwgtor of an object is directed anti-parallel to the velocity w8/cop7 wg p)x).vkep6-*wje mipi (h vector,

  If the acceleration of an object is always directed perpqugkyx.ldqh2 nyzf w -;2.2.pendicular to its velocity,;w2xg qp f.lk.- ydhzu2nq 2y.

  At what angle should a water-gun be aimivgmmw9*5( yqm mxr(*c,xby1(*m dq red in order for the water to land with the grea ( rw( mq19xqcrxd my* im(*v5b,mmgy*test horizontal range?

  An Olympic athlete throws a javelin at four5i2cct*pv4. o .xpe ztgu+y-e different angles above the horizontal, each withz.pteex- y.+gp4ci5 cvu2ot* 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 3 6zztupjfx;;i0lj9 it7z 7wti 0i xf1your hand with twice the velocity it f9zx7 017ilwji tt6;it 0xupjz3;i zf had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an origi*c,9sm7bfo;sg cyy qla; i)) anal 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 field goal attempt reaches its maximum hei .vl/nc618hvauz x9xoght, how does its speev xz.1xlh9n/6 ac8v oud compare to its initial speed?

  A stone is thrown horizontay 75k8 : t;krpoeto(sdlly from the top of a tower at the same instant a bal:or 7k5tt o;(ey8ksd pl is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired hoym t/+m+ge3xxrizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Com/e+myg mxxt3 +pare the times of fall of the two bullets.

  A plane flying horizontally a1 umh3oo ;v6.dvwjn4mt a speed of 81.4 m/s and at an elevation of 173 m drops a package.4hmv;u36jw mvno d1.o 2.6 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:n d*15xf: ;im(, pf t(hiagbje feb;l a second packag *h df(ft5p:la jbng;,mb x;e:( fi1iee is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally3j(utzbix-f7j 3 r;k 9egki0 g at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizz-jgk 7xgjb ;tikur93e i30(fontal location of the plane will

  The acceleration of gravity on the Mig0:jj, enn )6q/x4 yf+vjyhsoon is only one-sixth of that on Earth. If you hit a b)6,s jyixqv / 0egnh4j:j +fynaseball 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(o yz (w);i lskxqn0v4 +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The ro(z wq) (kxyn0l isv;4elative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong current.vg,gtpv /cl09 You start out in your motorboat on the east bank desiring to reach the westl9 gpg/v, vtc0 bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How muc r e6q vlk9scc.7tlw-(h time will it take you to move 12 km downstream, in a river fl lvetqrc-w k6s(c.97 lowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. b4x3 (r3ps wxtps5hu5 The y compo5(subxt3 xh5ps 3w4p rnent of A is

  If a ball is thrown with a velocity of 25 e:vh. hk dl,8qm/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 direction nor+o*g,so ) upveth of east and you end up 2.0 km north and several k ,+)pouvgs*oe ilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity i-ch .) sho9gvgndq z()s 8.00 m/s. The angle between the direction of its moz-)v.hgq chg)n o9ds(tion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over ad(x1iapr33.nb h7b9brh(3 cf8hv rh p level ground. At what angle is 3(h pxdhb( br33c .ph1r7av8rnibfh9 the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What o jho3r4s4a)obka;8h are the components of the sum of thesas o ak)h3 b;4o8h4jore two vectors?

  Two vectors A and B have components (0, 1) and (-1,k;6ex-k8 1gqhfwl de , 3), respectively. What is magnitude of the sum of these two vectors ,l1 ge w8-xefkkdq6h;?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + *2zm8mi;wu1r9 g hlxrx-+qim,x nl8n B . What is the magnitude of 88nz;m2xigr-iuql m x w*rnm+19lx, h C ?

  A car travels 20 km West, then 20 km Sox7 7e2.dqvf o3r849fyv1 qb .wmx gnuxuth. What is the magnitude of its displacement?4vun fxw7d .7b x9q1vo83xf2gy . emrq

  Three vectors, expressed in Cartesian coordinates,wy( tdw/s )eobupxm x5/-p96w 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 coordphx2axv7/ bqi+cg8io9bbsyoy- k274 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, -8.0), what is the magnitudni3e9eqail 3r +y. *h6huyjx (e of iyhi+*eeq ux9.ry(lh36a3 j nvector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. W,n :tv1fi; r kece65ubln;*yohat is the displacecryenfbo6: l;t ;iv*n k5u,1ement of the jogger?

  Two forces are acting on an object as shown in F k0y57xy)ls - .oie jb9gr-pkpig. below. What is the magnitude of the resultanj5ey97g)i-b0 o -prl y.ksxkpt force?

  Two forces are acting on an object as shown in Fig. below. What is the directio tht mrv6)75isn of i7 hm)t5svrt 6the resultant force?

  Vector A is 5.7 cm long and points aes tq9j -)a .ib)wr,uh8ar1l ulong the positive x axis. Vector B is 9.7 cm long and points a ra8 ibu).-s1w lh t)e9qj,aurt $+58^{\circ}$ 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 65 cm long and pointsm4 9ukeef9) dtd0h4iq at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 48 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 26 m/s from the 7/ caweg1vv v/edge of a cliff. A stop watch measures the stone's trajectory time from the top of thc1eawvvg7//v e cliff to the bottom to be 3.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 17 m/s, from a bridge. It d c qv e6k4vu79bz3s0eu4)xel falls 19 m to the wate3 exqzduul7sc 4 04ebv6)vek 9r below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, strikes the gro u2 z0a8o36 ;ixvn0akbg(bb5p fzvye ,und a (0b b85v6zx2fzn;kb ieyp 0ga3,ovuafter traveling horizontally a distance of 15 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12g12rakgtm-+z7 p mm a60o n.vj m/s at an angle t amvnj7g.2- +zo 1m06akpgm rof $20^{\circ}$ 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 spe jhglc6q ov4qp6 u(rf)i.-2q m)-5 egz5vlvbp ed of 8 m/s at an angle of)6pv)z -(j2rvulbhgel .mv qgq 5iqc5fp6-o4 $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 48.88p4-145wz e fagwyb1wzg mn1w m/s at an angle of $45.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of ; k4ds 6amknhbi8+pek/ ; 1orf59.4 m/s at an angle of $33.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ukoh*:-1m2jdvc9m x0vr- o h sangle 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 7pp d+z.bw-netck 3+ m 16.7 $m/s$ from the roof of a building 35.3 $m$ 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-n w4sqarxo-6ed of 47.1 m/s at an angle of w6oar- 4 qx-sn$40.0^{\circ}$ 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 rac:l7f uwff 51 -s/ crnmkopj82ye at a velocity of 4.0 m/s. If you ran the same race on a day when you had amj:w-81f o2frnu/yp 5clk f7s 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 mwp2zps (wve0v 4,(sq a/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relatives, pv(pvsz4(w w2a 0qe to the ground is

  A plane is flying due Sout:p)ktd p4+ o/cww qg2ch ($270^{\circ}$) 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 h h 8 ixl0+pvdq75obxjz6,x*q ieaded $30.0^{\circ}$ 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/ pqrz 5ua):jw;s horizontally fires a projectile with speed 50.0 m/s in a forward aq;5j)zu: rwp 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 wtyyf 7zf 7:xt6ith a cufz 7tf7x:yt6 yrrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 meue*ai/ttc /:w .ur5v /s in still water wishes to travel directly across a river uut/ :ic. *reve/wt5a 1.1 km wide in which the current flows at 4.2 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 wi3 h3 vc zoblah.m.*:zghxjd9/shes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what3 ov*.cx3d : mh.hbjz9 /hzgla angle upstream should the driver head the boat?

  A swimmer heading directly across3ob57f.a vth e a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstrhae 5fo. b7tv3eam 480 m. How fast can she swim in still water?

  A swimmer heading directly across 7e8j s7ukjj8 oa river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreauj 8j78j7eosk m 480 m. What is the speed of the current?

  A boat, whose speed in still wathj ej0i,g u e*qi;1lr)er is 1.20 m/s, must aim upstream at an angle ofrj, gu)elij0 e ;ih*1q $17.0^{\circ}$ (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)  $m/s$