Which one of the following is an example of a veib *k7p1h *ookctor quantity?

  Which of the following opbcf u+ rp(t-g-ah af5-erations will not change a vector?

  Which of the following i-vbit2t tuy3(s an accurate statement?

  The resultant of two vectors is the smallest when the angle betwee2a ) iy8+zxoedn them is

  Two displacement vectors have magnitudes 0c7d2iq-xb cq (oqkq j(,n,idof 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitqx ,7dki j( cqn,-qc0 bq(di2oude of the sum

  Two vectors, of magnitudes 20 and 50, k0r6ai xkx5w1 h/4vazare added. Which one of the following is a possible answer for t1/ xa6xwi5kr0v4ahkz he magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an 2rdh 9b8nb0jk object in directions that areb 8krj09b dnh2 $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec)4 t,u kv/xxn4gwbel oow,6)4f1vpwator is

  Ignoring air resistance, the horizb i*uso1o ) 4qoems19eontal component of a projectile's velocity

  A ball is thrown with aa we+c9x q8bvur8v p) op7.:tm velocity 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 acce;u1m6sl4aj6 qs+wkto c: m xu0lerationsjm6 mks4 +:ut1uw;x0la6 oqc

  A soccer ball is kicked with a velocity of 25 m/s at an angl9st vb v21mt3soowguh b*y5uyrh81 6l*q5-ple 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 directedpixzulr(rwd6r+w( d 2q+w/ /m anti-parallel to the velocity ved rm (/ r(+xqizw+dl62 wruw/pctor,

  If the acceleration of an object is always directed perpendicular to its velocir 7pyti8vw+p-k. x +vtty, xppr-ytvwi+ v.7k8t+

  At what angle should a water-y ;2* sz k4mcug;fpd,tgun be aimed in order for the water to land with the greatest horizontal2 pu;*,d myf;ksgtz4c range?

  An Olympic athlete throws a javelin at four different awzq6 lp;;am d*ngles above the horizontal, each;mal*p;z wdq6 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 time. If the ball leafm 6ue9ga8+tt. vug- aves your hand with twice the velocity it had on your firsta+g u. -e8ft6gamu9vt throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an k1l(sx.aw- z, zzz9tpangle 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 maximumq;* 9b,4fd+0+inftp3rcoa1t ka sobb height, how does its s1o0aqo+;sb ntki 9* r34fpbdc,f ab+tpeed compare to its initial speed?

  A stone is thrown horizontally from the top fwnob5k:0-se of a tower at the same instant a ball is dropped vertically. Which :o -s0bwfenk5object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, : 4nudg hx, pr(brxd:)and at the same instant a second bullet is dropped from the same heighpn,h:br gd:urdx(4 )xt. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 70.9 m/s and at an elevation of 17+r(s*q( kj ojp7 m drops a package. 6.3 seconds later it drops a second package. How far apart will the j*qors k p((+jtwo packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a secmd+/ 2t0 cstx2emzly8 ond package is dropped. Neglecting air resistance, the distance between the falling packages wi cm2 st e2t+8m0ylzxd/ll

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Negl y;7)ql(mqq ouecting air resistance, when the bomb hits the ground the huml yq( ;oq)q7orizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth m+vgjm .1 mpi/of that on Earth. If you gv/ +mi.1mjmp hit a baseball 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/hw , tehj)a8(epq2(3s/bq pnmn in the +x axis relative to a straight, level road and pass a car travelin)8nwqq(h ebj( ,p2/ nsamtep 3g at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south witrs 0 hectt(::l46egk2 piu:mj) 7nwcth a strong current. You start out in your motorboat on the east bank desiring to reach the west bank te l:r0hknj cpu:7gs42me(w 6t) c:itdirectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. H boz4m(4d,(izp3fo0ada t6 s tow much time will it take you to move 12 km downstream, in a river (to(34m4 fia d,db zop st6z0aflowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the v7s,57bdq: / yejuvml +x axis. The y componem vsbuv75jyl/: ,eq7dnt of A is

  If a ball is thrown with a velocitynag5pqnu0ur/a..l m t a6j35n 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 aas3-6vysaf ;g)j(cww straight line in a direction north of east and you end up 2.0 km north and several kilomcs6 j3aav( wy )gw-s;feters east. How many degrees north of east have you walked?

  A butterfly moves with a spee r4asqqgmqp 54caz8x3w2; g0a d of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direxg8z rg5 p40am 2qqw4a ;s3qcaction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m louhs qgf-b95- zng shadow over a level ground. At what angle is the Sun elevated above the horgzfb5 sh-9-uq izon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivlxen2st4( a8ia * v,pgely. What are the components of the sum of thesiav4a28ns,l x gp*e(te two vectors?

  Two vectors A and B h(6w8mm6fiw kp ave components (0, 1) and (-1, 3), respectively. What is magnitude of the s6 p(k8wwmfm i6um of these two vectors?

  Vector A = (1, 3). Ve yb9o+gjg8 r -0 +llnb3as)nmkctor B = (3, 0). Vector C = A + B . What is the magnitude of C ?83j+ka0 mb+ysno g9-)llrgn b

  A car travels 20 km West, then 20 km South. What is the magnitude of its displj2 qr(2nh yaidz. 0,ij+jem zrti8* /vaceme /82in (a0jyjv+2z edzrhq*imi tr. ,jnt?

  Three vectors, expressed in kl*:p,tbcy*qbr1ox9p58)-/w p y iz8 z pxexkCartesian 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 s78m7l-boyv ,-cxrojCartesian 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,d1xh6f,b jpx B = (+3.0, -8.0), what is the magnitude of vector Chd6,x bp fx,1j = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the displ db 1faira8-lk6fdcc4 ygt:0lr8 e+ 1vacement of the jayl- r1a+r8d:cg 4 v0k1f tcdeib8l6fogger?

  Two forces are acting on an object as shown in Fig. below. What is the::xivpk; kfxml fq4f) utq:1+ magnitude of the resultant4 :vxupiq +qf :mf f;:)tl1xkk force?

  Two forces are acting on an objew8w.rx4noj ,( p1wuoit q u:1ect as shown in Fig. below. What is the direction opwue1n,w4u :1t 8j oir (xq.wof the resultant force?

  Vector A is 5.0 cm long and points along the posscp5;flmn- 8b17vi ez itive x axis. Vector B is 7.9 cm long a-p f;ne8m 57 bs1viczlnd points at $+28^{\circ}$ 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 74 cm long and poin w iwudk-(e3g6ts 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 horizontally with an initim+aiweg-i kv(ud8bm/ j.oe ( ,0ahxo )al speed of 13 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top o,e-ok bam8+ gjm .uh 0/xwv(ia )ei(dof the cliff to the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocityh4p x /vm2:vpmr2tc n/ of 7 m/s, from a bridge. It falls 30 m to the water belowprt/mp4mc /: v2 hvnx2. How far does the rock travel horizontally before striking the water?

  A ball thrown horizoz-(iaah z 8,ijq 9yjk5.+a uszntally from a point 22 m above the ground, strikes the ground after traveling horizontally a zya- 5 j.89suiaiz kh,a( qjz+distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into 6ks.k+ vxfah ,m ,lexy/+/y4 o(fqmxwthe jump with a speed of 12 m/s at an angle ox koh++ fa,y,el /mwy(sv/6x kq.mfx4 f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the longd.5 h/bk r/2-lxcshki-jump goes into the jump with a speed of 12 m/s at an angle sl.ki/x hd/kh-b2 5 crof $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wyrmh)4i g02pz2 ed oit f+g::cith an initial velocity of 26.2 m/s at an angle of $10.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velz,j.oq--a ) x,iqv vwdtlnw* ;ocity of 37.8 m/s at an angle of $44.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of fc4xt9hkw )gc:dw4o*pfj 2:f $30^{\circ}$ 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 horizonz8g6hull b31 vtally at 26.2 $m/s$ from the roof of a building 50.1 $m$ 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 mtgp *x5k8440.;8wze- oc n-hbrwg cn bdtk(o of 55.3 m/s at an angle ofg488 mc ( n oho-nx-;tetrb*kkzbcp4g0w5 .dw $44.2^{\circ}$ 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/*/r 0m.l0 0deshjmfb as. If you ran the same race on a day when you had a constant headwind which slowsdm*s bm/0f aer h00l.j 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 North,fdgoiqr //)kl ( dgicl;.jz;2 and is in a wind of 50.0 m/s to the West. The plane's speed relative g j 2lkd.rdg lci z;o)//qi;(fto the ground is

  A plane is flying due p. qh-n1s++u)ac eojb South ($270^{\circ}$) 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 1ebvbu +d*)id14;hy2hff2 fy.p6km pn 20 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 sp f7 y q3txx.h6fzpru1-eed 50.0 m/s in a forward directiontupr f.h-1yq76zxx 3f $30.0^{\circ}$ 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 anh5p2r jnco ,e2 rmdxz983ck/ river with a current of 6.0 m/s. What is3 r/czjxhmk2necp2d or 89n5, the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 12 m/s in 848 k(a(yk imgrkne.v still water wishes to travel directly acrossek8irym gk(.k4(8 nva a river 1.3 km wide in which the current flows at 3.6 m/s. How long will it take to cross the river?

  The driver of a moto.s i;m+j 5qktmrboat that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flomsij m +t5.kq;ws 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 opposilcj,/wpge:5w te bank in 6 min 40 s. She is swept downstream 480 m. Howw5w:jclp ,/ eg fast can she swim in still water?

  A swimmer heading directly across a rc07hz) ;ritufti sy *3ej +6pciver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the cu t;jt 7ecp3ifsy i6u)c*0zr+hrrent?

  A boat, whose speed in still water is 1.63 m/s, must aig;.hs +d8ms c6ow9y-7itwhere3wde7 m upstream at an angle of3s - e7ihe mw ct8;rg.+s6e7yw dodh9w $31.0^{\circ}$ (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)  $m/s$