Which one of the follo0rf x/e7/md(k q w+bzywing is an example of a vector quantity?

  Which of the following operations will not c9: sd(ztliizwrc (0v/hange a vector?

  Which of the following is8tn*mx-;h2jv,b *3kwptl/rr lsj1 fm an accurate statement?

  The resultant of two vectors is the smallest when the angle betweeyk(:yaq0aexj dywlq:2/m5 f 7n them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respecti6 ldhf/y *f 7c n4sqjz17mob(wvely. When these two vectors are added,4smq d*6ch( 7yzb1/ol 7wfj fn the magnitude of the sum

  Two vectors, of magnitudes 20 ajlo t*rv fbgyq2 ;e10+nd 50, are added. Which one of the following is a possible answer for the magniotqb+0jyfe l2g*;v1 rtude of the resultant?

  Three forces, each having cbm3ct;c ) 8*l uhq5f/flem;ca magnitude of 30 N, pull on an object in directions that ar u*t /cl;c8f;5mb qlhe3m )ccfe $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, th; ub/nxn4pmx.3 bgf.be unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's va874 heizizcv 0o9(tea5.akk9c fep +elocity

  A ball is thrown with a vel:pl 9bmy9eh .;9cphv fb(pn8u ocity 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 projectile's mrt ox7 cyj6+4accelerationrm74+6ct jyox

  A soccer ball is kicked with a velocity of 25 m/s at an angle 12gv6ng t400hs menroxl74 iw 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-parallel toa /id7pp0:mo cx3rw(x the velocity vector,3 iraxm7/wopxdp :c(0

  If the acceleration of an object is always directed perpendil9ose-3bkj k/ahyz : 5cular to its velocity,kb-l:ez5a yj ok39h s/

  At what angle should a water-gun98bpcef4nvlcyrtd blc4 ,9+1 be aimed in order for the water to land with the greatest horizontal 4b89 + dflbv crnpc4ctl 1ye9,range?

  An Olympic athlete t43q fog ldkm,1hrows a javelin at four different angles above the horizontal, each wiq1k4mgo l,f d3th 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.3hm *8xkp ctclv/z9jme. If the ball leaves your hand with twice the velocity it had/zhtcl. 3v *cj xp9k8m on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spee1wkai y.u n; 8;vmm+ad15ho/udfcjy: d 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 height, how does i7 tt6uj o80iepts speed compare to its initial spee6te8pj0i7 out d?

  A stone is thrown horizontally from th3 hw7*gdv45c1q-yxacig : nnle top of a tower at the same instant a ball lig:*1n nqa5 4dvgc73 -hxwcyis dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dropao p4l ; a49gx9jtab6lpb;x49ll9ato pg a46ajed from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizont1y+ 1uvmhapy, ally at a speed of 102.0 m/s and at an elevation of 129 m drops a package. 5.7 seconds u 1yp+yam1 vh,later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped fromom:ih -5y jj:s a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the :oih:sjm5yj- falling packages will

  A pilot drops a bomb from a plane flyinf3rlnk ezl:.;06 tswoj ep7h,g horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane willl st,lw: 30ef7zr nje.p;kh6o

  The acceleration of gravity on the Moon is at ik .3;;o oh qbbytten,(84 )ujiy.fonly 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 landthyi ,b t3ti yfn8; .beqj.)(au k;o4o

  You are traveling at 55 mi/h in the +x axis(ht5 mboc z2c)p ogsxq t4j h:/4g91ts relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your ca2z 1htm s joc9 os)4b4(pqgc5tgt x/h:r to the other car is

  You are trying to cross a river that flows due south:o3 m( i/b2d5.ocqmqsctewk+ i enhag c/-,y/ with a strong current. You start out in your motorboat on the east bank desiring to reach the/kb:miy qdm. w/2nc 5qi-(a3,/chs eo+e goct west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Hi53sr .4u4oq dtqhuf8ow much time will it take you to move 12 km downstream, in a river flowins854. 4qrfuht3 d uoqig at 6.0 km/h?

  Vector A has magnitude 8.0-mai .ru w3p;z m at an angle of 30 degrees below the +x axis. The y com;ia.3rpw - uzmponent of A is

  If a ball is thrown with p4kifjl; ))xk)ni)d k a velocity 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 end*ser8geao+jg87 )e;a yfl hk- up 2.0 km north and several kilometers east. How many degrees north of ea8g*7e8a jo-h lr)f yk;aeegs+ st have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its v6c) a ymgy:p9velocity is 8.00 m/s. The angle between the direction of its motion vyay)mpgc 6:9and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level groundp w7yz3ke)c4sr95 w+ fv soo,t. At what angle is the Sun ele)svye5pok3 s,7fo+c9w wr z4t vated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What ar*j c)g/e *o;ougve ul :9orpw+e the components of the sum ofe+/vpegc);ugulow :o* 9 rj*o these two vectors?

  Two vectors A and B have cojhig6ul/;.2lhkv vv, mponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two.u,l;ivhjhlvg 2/ 6 vk vectors?

  Vector A = (1, 3). Vec4 *u tejk6)0jnyv :mkutor B = (3, 0). Vector C = A + B . What is the magnitude kv*t:e 4ju0u jm k6ny)of C ?

  A car travels 20 km West, then 20 ds 7ykb;lzm.a h )r(9wkm South. What is the magnitude of its displacw (bdhzry9k am;7sl).ement?

  Three vectors, expreg*tzs 5lka c00.*n vtgssed 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, expressed in Ca1c3f:gf t jc0mrtesian 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 vector B = (+3.0, -8.0), what is the magnitude o(5jbu7k fa9zc f vector C = A 9fu bza(kc7j5 - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dk5e0ky knifakvgf-dx 0)- x;:sv 7.q tisplacement -k ve0k7vt f-.kxg:)dsni;k qx5 0afyof the jogger?

  Two forces are acting on an object m18h7 9lro vguas shown in Fig. below. What is the magnitude of the resultant force78 ml1hg9rov u?

  Two forces are acting on an ob h ux;k171pnjcject as shown in Fig. below. What is the direction of the resultant fo;xkjn 17pu 1chrce?

  Vector A is 4.6 cm long and points along the positive x axis. Vector B bv hko:n(k9)ms,hm 3 mis 5.5 cm long a mhbh3m ),vs9(:ko kmnnd points at $+31^{\circ}$ 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 84 cm long and points at wd 6) 2/ g2x+fo kpfw+svpngr8$30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 49 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 horizontally45;xig c(stxvp-i de* with an initial speed of 14 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 4.9 s. What is the height of t-xi s;5 c4d*(tgx pevihe cliff?

  A girl throws a rock horizontally, with a vi gea*6n(2w rrelocity of 10 m/s, from a bridge. It falls 29 m to the water below. How far does the rock travel horizontall ngi2rr(w*6a ey before striking the water?

  A ball thrown horizontally from a point 21 m abolsna j kg8ct9s070- ujve the ground, strikes the ground after travelingljc n89aku0js- s0 7tg horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goesf ius( i89u;:vy ect5t into the jump with a speed of 12 m/s at an angle of vt s 8ficyteu;59u(:i $20^{\circ}$ 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 oym-cco6942g0v f i5efrz u ,jkahh5 2kf 14 m/s at an angle of aochg5vhy0 6fue-2jmi9f2 cr ,k5 kz4$17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 48.3 m/s at wf9cam (7d; uyan angle of $23.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vikth3l : 2xi*velocity of 36.1 m/s at an angle of $44.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedtehume x s;9tv82ax e q85soz)(dhi(. 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 atkrcr2 (j( + clwl9;mjj 26.8 $m/s$ from the roof of a building 67.6 $m$ 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 level with an initial speed of 57.4 m/s a+-9drt,cyj.a:*r(vmq wo m w at an a: rwrjyca( v9ta+m-wd.* q,omngle of $45.3^{\circ}$ 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), you can run a 1500-m race at a velocity of 4.0 mc59p5zqs5c z 8f ywo+e/s. If you ran the same race on a day when you had a constant headwqw9o5p5 zzye ccf+8 5sind 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 2 ap0 e8s:e/d f/x(44rnrprphu00 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grou:rxsefpahp /r(0u4/e 4 r8dnpnd is

  A plane is flying due Sh/(i 9cl ch-xfddhw,6)q ct6houth ($270^{\circ}$) 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 kz* rp07p6ojcwyoxf rk6/h 2u3 m/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 ;v-: q*ilg/dzx g hr0phorizontally fires a projectile with speed 50.0 m/s in i*;g0/lzxp :r g hqdv-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.l3+ ngtrnrw jh1(ek0-)qt e+ b0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the b ( nq3lrk)+nejt0+egbr-ht1 woat as it crosses the river?

  The driver of a motorboat th;rebj(8o /tls at can move at 18 m/s in still water wishes to travel directly across a river 1.0 km wide in which the current flows at 5.9 m/s. How long will b/8(tor es jl;it take to cross the river?

  The driver of a moto1 o.raz8 3*u(kqf+n.8mrlnt(c gvnxr rboat 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 n(r1f3nz+8 ua g* kq.(o. vlmrr xntc8driver head the boat?

  A swimmer heading directly across a riverkwol3q p5zk -. 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast cank. kowz- 35lqp she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank (/vo0 k;t 5twpxtddfi i re0;;in 6 min 40 s. Set/5t( v;xt;ro ;0iddip0w k fhe is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in stilr8z ba -9;+tgnqhf7bk 2ipwz536lu lsl water is 2.00 m/s, must aim upstream at an angle of-a 3h257f9br z8 z+s tlglqnup;ikbw6 $21.2^{\circ}$ (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)  $m/s$