Which one of the following is an exampzw x 04sve4ob4le of a vector quantity?

  Which of the following operah 6h.s x)wz6puy9 o *f:pconc)kpi/*ptions will not change a vector?

  Which of the following is an accurate l*ckgl h6*tb1 statement?

  The resultant of two vectory:h6nv +c/e iys is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivelmnx .+ c sw-attkf7*+ry. When these two vectors are added, the magnitn*- tstrxwc7am f+.+k ude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followi87 now ,dm2b 5dlykm/th42e tqng is a possible answer fork8 q ld m4hdmb2,y7wte t25on/ the magnitude of the resultant?

  Three forces, each having a magt/edbiw 8+t h0nitude of 30 N, pull on an object in directions that are bi tht0+wd /8e$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowk ko/6 cbw8ok:n vector is

  Ignoring air resistance, the horizontal component of a projectile's velocitym4 3qq)e5if cl

  A ball is thrown with a velocity of 20 m/s at an ang g9/c 3hfjggk 1a*iwa*le 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 projectif*s+k+8 19ojxazgw oq fi; 4bfle's acceleration;kf aijo1f84*qg9wxzf sbo++

  A soccer ball is kicked with a vww e 0:u4sel52hzk :nmelocity 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 vector uqa mz9skx .0t21hf n+of an object is directed anti-parallel to the velocitsnthqax0f + k1 92.muzy vector,

  If the acceleration of an object is always directez;)bh 8j ob7x acwayo 97vqo;6d perpendicular to its velocit)oc7a96obzvjw8x oqby;a ;7hy,

  At what angle should a water-gun be aimed in order for the water to land with th3huifx cg0fq)whgxjq)y)l;; 9n 2fd7e greatest horizontal range) )ix0)wjlgqn ;ghdu9 f hfxq 37fc;2y?

  An Olympic athlete throws a javelin at four different angles above theqfe (2m* oqp:h horizontal, each with t*2(epqf hmo :qhe 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 secowm *y467qc90 qmej0ki i-yz;.un kigz nd time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal rang ncmey7z-ii0qu9g k4;y0q.zjm*k6iw e R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle l7 (5d4fm4 xd*jvsdneof $35^{\circ}$ 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 maxpge ez7am9 :kk-q+l1iimum height, how does its s-lm7eea: zq kp 19kig+peed compare to its initial speed?

  A stone is thrown horizontally from the top94;paxu m j;uw q8cy/dv qi1n2+a vnn0 of a tower at the same instant a ball is dropped vertically. Which object is trvqaq42+; dmn x/nny8a 1vcu9pwj0 ;iuaveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same insta21ejm4vllbo2 hgo0v ;q0k x0j nt a second bullet is dropped from the same height. Ignore air resistance. Compare the00lhm j2vlx0je;vo4 bgqok12 times of fall of the two bullets.

  A plane flying horizontally at a speed of 73.1 m/s and at an ele91f gpn9(-wy5umx wjt vation of 170 m drops a package. 6.7 seconds later it drops a second package. How far apart will the-wt wgxjpm15 yu99fn( two packages land on the ground?

  A package of supplies is dropped from a p l98g )j .z;hblrzxu2slane, and one second later a second package is dropped. Neglecti;l jg9 s)zlz 8.bh2xurng air resistance, the distance between the falling packages will

  A pilot drops a bomb from f8)cgtbx4c l)0 4 u,hqhrzy)na plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb ht bfn))gc0x) qyrc, zuh8 4l4hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of th(sd2yg+0 t5:h qb kxptat on Earth. If you hit a baseball on the Moo0qx+ts d 5p(t2bg:h ykn 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 +x axis reg j 0d:vra 4e-b*ueq8plative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your 8e: 4dbe -0qupr*av jgcar to the other car is

  You are trying to cross a river that flows due south with a strong cu fo- biec9,8m fpwt*3crrent. You start out in your motorboat on the east bank desiring to reach the west bank directly 3ope, wbt9fc- cmi *f8west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How mukg afdq5nh/8 w9wa5 c;ch time will it take you to move 12 km downstream, in a river flowing at 6.0 kw9wq5h a;c/ n 8fgakd5m/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below th ygfd(lp (hris0+j j7ya0/j a:e +x axis. The y component of A j y0alyi :rj0f(+g(pdha/ s 7jis

  If a ball is thrown with a velocity vez gfk+zya2y9135(+nru8k i nbdv:a of 25 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 straight line in a direction north of east and you eniceo* ;p rvgz/ik4h;z)e)v 7 yd up 2.0 km north and several k yk*e7z;v/ i grio hvz);)c4peilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed + 9j-g-v.cod9n q .(nqmikmqb7uqag6 of 12.0 m/s. The x component of its velocity is 8.0o(nqmgqa.9 cjb9uqvq-n-k gd6i+m7 .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 shadow over a level ground. At what6z4 h)aq5 ekoy5sldms9)t *mk angle is the Sun elevated above tm)e5qo64 )akt s 5zskl*9hydmhe horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivr.v(zj(e+u6bgce t zh sqwr( v5u6z0*ely. What are the components hgub(r6qv 5*zct.rsue( 06( z + ejwzvof the sum of these two vectors?

  Two vectors A and B have components (0, 1 fe :f2a:hth6x) and (-1, 3), respectively. What is magnfha: ft x:eh26itude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vect/04 4e*xjjec8a oq biuor C = A + B . What is the magnitude of C o 4buex jeqa48 c*/0ji?

  A car travels 20 km West, then 20 .tl 4tk t+k*epkm South. What is the magnitude of its displacemenkl t *4+e.pttkt?

  Three vectors, expressed in Cartesian co,qdfc u1v1b(d va.y9 gordinates, 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 coordinates, azg9+k6 ( yupwsatsa)6 re
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, -e -ch 1nkes*ga8up49pmal7if,.u1 l v4.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A g af4v71 l.,such1k luneppm*e-ai9 8- B ?

  A runner runs halfway around a circular path of radius 10 m. Whab eu3j-3wbyz .t is the displaceu-3y3ze wb j.bment of the jogger?

  Two forces are acting on an object as shown su vx 3sq(, 2s ,zuhga/8bkk2lin Fig. below. What is the magnitude of the resultant fg,qs2a2 kv3uhx 8l/kssub, z(orce?

  Two forces are acting on an oztlg3:e*yo3ra p r.)c bject as shown in Fig. below. What is the direction of tyzr3:.tcelo ) 3r ga*phe resultant force?

  Vector A is 3.7 cm long and points along the positive x axis. Vec-6 mqx(l/ fmtrtor B is 6.0 cm longmml/f t6q(x r- 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 62 cm long aqi8i; ntjc5 xlm4f1s/nd points at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 34 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 horizontallyyvnq p-rpqdkrs 4ys 5x9-4(e7 with an initial speed of 18 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 4.2 s. What is the height of the cliff?594py-sy n7krre 4q(dvq-ps x

  A girl throws a rock horizontak7eto 2;7h-xoke;gj /u xu2d nlly, with a velocity of 7 m/s, from a bridge. It falls 21 m to the water below. How far does the rock travee2du/2-ex ujg;n ; 7kh kxtoo7l horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground,ml )q5 vl9p8t-py gkd5 strikes the ground after traveling horizontally a distance of 21 m. With what speed 9y8)tvlp5 kl-qdgpm5 was it thrown?

  A jumper in the long- (jddh 3 xv6r*s4cc-fjjump goes into the jump with a speed of 12 m/s at an angle dv( cs3dr*4 h fj6cxj-of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump53tz wwddc, 1(izx4n9i drwplx1t 9c6 goes into the jump with a speed of 12 m/s at an angle of r 5 (lxtcpwcwd3d ,i tz6 dinz99x1w14$29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wi -sap5qf( gb6 b.te9oaxdbr 43th an initial velocity of 21.0 m/s at an angle of $11.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with tf1vubuj.-+0 lf*9q ytgi8 ajan initial velocity of 58.9 m/s at an angle of $39.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firei zzp.7 a(hs1yqe c,;1tvph .fd at 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 1h/ o;bhp;,q) 0gr-iuh3 lxveo9.1 $m/s$ from the roof of a building 40.9 $m$ 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 o6g* ;tw psysn3hcm7 +kf 55.6 m/s at an ang7wm3+ygcs n k6*;ps htle of $42.8^{\circ}$ 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 veghvnj*ymyfl , ,v;;r; locity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your s;h;,n l*jyg y;vrvm f,peed 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 d(8fmlkd3zw v 8ue North, and is in a wind of 50.0 m/s to the (kf w38zlv8md West. The plane's speed relative to the ground is

  A plane is flying due South (rhb1pj1 y 7metn t.n ,tgpu24-$270^{\circ}$) 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 3( 0k2urkd h*)qeonefheaded $30.0^{\circ}$ 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 movin;.m oeog1kfy e):1za s9-b7/0oenwr5s ozvo eg 200 m/s horizontally fires a projectile with speed 50.0 m/s in a forward de;/r1o0m:a- y9wookg szee75vz bo 1 seo)n f.irection $30.0^{\circ}$ 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 a c4xdsug6.(xq,uqqywte/h 0 1cross a river with a current of 6.0 m/s. Wha4.td6qgu( sq,/h0wycue x qx1t is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 9 m/s in still water wishes t,d/-)9lbx0q, ph wwvo nc fhq2o travel directly across a river 0.7 km wide in which the current flows a q/ ,w b9hln-dphwqx0vc,)o2 ft 7.4 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 wishes to traver aqmm/ ;0b( p o5dxf)y:h+bzgl directly across a narrow strait in which the curreq:od05h+r xm mbab;/zy g)(fpnt flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the w)be c0tq5 dtbf:-r1g opposite bank in 6 min 40 s. She is swept downstream 480 m. How fas t:fbtg)5wbe-q1drc 0t can she swim in still water?

  A swimmer heading directly across a river 200 m wide nz0: 3dyswg+ni+ zn:-t : r/hyszru-w reaches the opposite bank in 6 min 40 s. She /3ri y hnr+:uzs t :0w:gz+dysnwz --nis swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.19 m/s,*, pcg lso* ep)7g4jbe must aim upstream at an angle ofe *c 7le,4ggposj *pb) $20.4^{\circ}$ (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)  $m/s$