Which one of the following is an example of a vector quantity)py t (z3cpw(q?

  Which of the following operations will not change a vec1x/xmaax. bm,.9z kok tor?

  Which of the following is an accurate stateme+4wmn24vwsx ent?

  The resultant of two vectors is the smallest w uf)1z j,5ceuez8 zms(hen the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, res(urjy ; / modk)x/wa3oqd ybwl0:fz, 8pectively. When these two vectors are added, 8y/ujq3lod ,(wdxow)a:;yrzb/0 f kmthe magnitude of the sum

  Two vectors, of magnitudes 20 annr6:hn 06lmx2z9- bnfszw. uvq0 vw5vd 50, are added. Which one of the following is a possible answer for the magnitude o lw9x-h bnn0 066v5snuvf r z:.2vzwmqf the resultant?

  Three forces, each having a magnity0p0zke; k uygl9m.k c+do.f 3*bme(+ug 3rdwude of 30 N, pull on an object in directions that a o0ufk dcpky*z .(+g eeyu;3d+lm kg. wr3m9b0re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the,z cc8gf1 byuswc o0w9tk3* gj.(a0 tc unknown vector is

  Ignoring air resistance, the horizontal component of a projec-h (i,8by jw r*zi)hlrtile's velocity

  A ball is thrown with a velocity of 20 m/s at an anj yjtsw)x0f/ 6gle 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 aslh )x0:hcyt hu .x31x projectile's accelerationhylx.3hx :usht0 )cx1

  A soccer ball is kicked with a vw+sq gt6.o5up 04ymlvbu0 w0 3czhg pdz-8 +qoelocity 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 of an object is directed anti-para1v 0 *yrzv-h adcah:b3llel to the velocitva yrb ch-d:vh01az3 *y vector,

  If the acceleration of an object is always direckf*kq*1p +q* p i byncu3.ag,4(rqlsqted perpendicular to its velocitfla*i *rg( bkus 3,14kq n*pqc.qqpy+y,

  At what angle should a water-gun be ai.l xqc/s/ 9ar1wnqj 6wmed in order for the water to land with the greatest horij ./qw c /la9xwsqrn16zontal range?

  An Olympic athlete throws a javelin at four different angle . npyfp)x+:szs above the horizontal, each with the pf. p: n)+zyxssame 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 bs **pf6a(f7-dc k wrz 9hs/beleaves your hand with twice the velocity it had on your first throw, its hori p h 6-dsb(9f/rwesfca*zk7b*zontal range R (compared to your first serve) would be

  A ball is thrown at an orilk4re l77hg f go0/*zynro +a70 wqv3oginal 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 h iac5ejjpu ,822fje5aa5 : ;j (xjtzezeight, how does its speed compare to its zpfae5 x: (2zcu;5jjet j5 aa2j8je,i initial speed?

  A stone is thrown horizontally from the to9x ts g(metb87p of a tower at the same instant a ball is dropped vertically. Which(sbtem 9x8g t7 object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and atlg gcv3o +(rfyc0l gp-z*5:v t the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall : +- tygc*lr0fzv5g(3gcvpl o of the two bullets.

  A plane flying horizontally at a speed ofkv*z(ky0r- t9sphn,tu8 bm9(l lyup; 64.2 m/s and at an elevation of 142 m drops a package. 4.3 seconds later it drops a second package. How far apart will the two packages land on the grouny;rl9t(sntpmbv k*pzy(-l 0,huk9 8u d?

  A package of supplies is dr;d:t7 e(ffj vdopped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling pdefj (fv:;td7ackages will

  A pilot drops a bomb from a pl)e5yusvf zhz6si-(e qx)u8d/ane flying horizontally at a constant speed. Neglecting air resistance, whe us (5qf)h-/d)e6z8svyeiz uxn the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth o 5irk(pb)m8lj f that on Earth. If you hit a baseball on the Moon with the same effort (and at the ski8r b5)( pljmpeed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in thep g5mq )le6ag9 +x axis relative to a straight, level road and pass a car t5pm6q e al)gg9raveling 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 with a strong current. Yos.h,akbv 1r) 3 o9biwgu start out in your motorboat on the east bank do).bhwak ,ri3bg91vsesiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take34o, 88z hxohusbas 7h you to move 12 km downstream, in a uozb xsah,o hs74883hriver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the8-6g opg;y4ho1 v9bduay hcd0hb752v7xozur +x axis. The yxu0y yorbv-ug 71pc2 hvg6d 5bhohzoa; d874 9 component of A is

  If a ball is thrown with a velocity of 25 m/s at) gs *i3m6yekd 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 ad suf/h9++tl . ;ivfxu direction north of east and you end up 2.0 km north and several kilometers east. How many degrees n xt/vfs;9 u+fu+.d hilorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vely7 cw259gferj ocity is 8.00 m/s. The angle between the direction of its mojy5ef7cg 29 wrtion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a levp thz4:b+l (y /,ynceg-ny9vjel ground. At what angle is the Sun elevated above the hori4czgy: 9(p b,vy+tl hnn/je-y zon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What ar0re-uynmip.0 el+ozb c b, 3a0e the yr- e0+,ue3a0b. mpbozn i0lccomponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiylcv: ( l;zpbe09. w+a9vsx aavely. What is magnitude of the sum of these two vectozv;l:eclx( 0ba.99yw pa+sv ars?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magniturba6fw1h9(o adf6oa 1wrb9 (ahe of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of ithhiqxzp8 s ,g -/-c1lis displacemen,pgq/si -ch1z8lh-i x t?

  Three vectors, expressed in Cartesian coordinates, b7;f8+wuoy2.vf2 eu t8fg ikdare
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 C-slg yupb , 7)sue4ynrs.2g3uartesian 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, -8.05gv: ,r;lr qjxnp7 rbw. uf.s7), what is the magnitude of vector C = 75j .fxwru:s,.;rvb7pg q nlrA - B ?

  A runner runs halfway around a cir 0:6(vt fx 9bt(w ,.fdldqsiwvcular path of radius 10 m. What is the displacementb, .f(9: txw v6 d0(twdlisfqv of the jogger?

  Two forces are acting on an object as shown in Fig. below.c* ylqwk0vd0 5 What is the magnitude of the resulw ck0y05*lq dvtant force?

  Two forces are acting on an object as shownote*/r s lpt-4gz(1tc in Fig. below. What is the direction of the resultant for ( oetg1 4z/p-tstlr*cce?

  Vector A is 3.7 cm long and points along the positive x9:s.1i ;c (jntr khmve axis. Vector B is 8.2 ccte h91rmvjk.n( ;:ism long and points at $+29^{\circ}$ 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 58 cm long and points ),5lalxat+d/hsej0s: tvy n 4at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 36 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 horiz.nr:n(6of z3vcp d y6ip;adf2ih y.w2ontally with an initial speed of 24 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 4.3 s. What is the height of the clifd2i:hio (.ny2rp66yzaw vf np3d c.f;f?

  A girl throws a rock horizontally, wit5*2vr z ,vvovth a velocity of 9 m/s, from a bridge. It falls 13 m to the water below. How far does the rock travel horizontallvtz,v5 ovr*v 2y before striking the water?

  A ball thrown horizontally from a point 296a(jm v)/if uq7jhao,p zo;/m m above the ground, strikes the ground after traveling horizontally a di7m;jf/qu ,j/i(mvo p6)haa o zstance of 24 m. With what speed was it thrown?

  A jumper in the long-jump goes into t9l +t5a 0vfd0*mqpj gfow8b4ihe jump with a speed of 12 m/s at an angle of pjt89md5l0ifwf0a*4 o vg +b q$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intr,+og k.k,igyczu4d 0o the jump with a speed of 11 m/s at an angle 0gzg+4ko,.kc iyr d, uof $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an ii +ciq/ b(+zu -a)6rfd9 aez5esf lv*nnitial velocity of 35.6 m/s at an angle of $12.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 39.4 m/s at an an9wa) 0 r9zj;fb4iruk ggle of $16.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an a4 a1*uww:v4af(v hhcongle 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 horizj: so *9g,ur;h(xfle aontally at 22.6 $m/s$ from the roof of a building 42.4 $m$ 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 67.5h g-.j ftl/1rhr ,hr-x m/s at an ar-hh.r,x1 ltrgj -/hf ngle of $38.8^{\circ}$ 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 velocitylq.ek5*/ yhjp3l8:h rk7rr ih of 4.0 m/s. If you ran th:i8q khyr r3lj7*p erh/lk5.he 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 finish would be

  A plane has an air speed of 200 m/s duea(rwbb.b -yi e +.z/wy North, and is in a wind of 50.0 m/s to the West. The pyber.b+/- ayw ibz(.w lane's speed relative to the ground is

  A plane is flying due So1r otx6l0g 1*wzv+stz* hjmr6uth ($270^{\circ}$) 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 4:iucw40tq jo 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 horz2+vrs:kqnk v5 ps24 9ast* piizontally fires a projectile with speed 50.0 m/s in a forw *9+k 5 ipa24:svqksrs2zpnvtard 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 r06fn0uyfaf05 9vtjem6vcq- zw 5y es4iver with a current of 6.0 m/s. What is the speed of the boat as it crosse m nz-05eatc0yvq4f56juff y evw60s9s the river?

  The driver of a motorboat that can move at 12; yv8tslpql09 m/s in still water wishes to travel directly across a river 2.0 km wide in which the current flows at 4.8 m/s. How long will it take to cross the rit8v 0y9sqp ll;ver?

  The driver of a motorboat that can move at 10 m/s in still water wishesl+ *qcoe zlu5ygbfx /;7y+wo3 to travel directly across a narrow strait in which the current flows at 5.0 m/s.g/u;ezob cqo3 y+lx+lfw5 7y* At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 2 wivcq5g(, )lt1i0 g g1b0mufwl ;hfo1 e2:jtj00 m wide reaches the opposite bank in 6 min 40 s. She is t ( fcj10:)vw gle2igmguoj501f hq ;tbw1,l iswept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly acrosdw2 wig/3ibnkz4: 5t52 wuquj urw:h.s a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstr2hzwq 453ib2uwwg ui/t k5rjn:d. wu:eam 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.99 m/s, must aim upstrea9ff zx( :ed/u k.-3kd1qvxc4.kr wsigm at an angle of 4(u3 kv.i f9e1-wd qkkfgs /. cxzr:dx$24.8^{\circ}$ (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)  $m/s$