Which one of the following i8a)7ltxg71im ei n5g ks an example of a vector quantity?

  Which of the following operations wy5 ot(1y;b tsgill not change a vector?

  Which of the following i8x (l(h:,1k irepjndls an accurate statement?

  The resultant of two vectors is the smallest when the angle between th2v /nnz qlx)4aem is

  Two displacement vectors have mag3gby(scr/ lg 0(cwf x+bd+n:gnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added3df/x0lr+n c(bywbcg(+ gg: s , the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following isy26fnf u8rol/ygo 1q 4 a2nfr 8o4y1 6gylqf /ou possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, 19vn+axc9cyji: b+ nepull on an object in directions thaax jb cn+9n+c 1v9yie:t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown jdspif/zbad2e;kxf22f *1h 5, the unknown vector is

  Ignoring air resistance, the ho hi,w nngtn-cy12k e9pet2 *.orizontal component of a projectile's velocity

  A ball is thrown wit*lf (l 9eis7pxdf :g3th a 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 acce1z(ty6 csa 6ulleration 1ay(z6s6 uctl

  A soccer ball is kicked with a velocity of 25 m/s at anjgy-1 ch8xh, 41pgzs v 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-parallel to the vel+u3hxs(o usxd (l*9xvx+ouwmp9+ ew/ocity vect s lwxsdvm3u9+ (hpw*oe x(uox/u++x9 or,

  If the acceleration of an ob)3 mh. kbtj(frject is always directed perpendicular to its velocit)bkf3t(rm h.j y,

  At what angle should a water-gun be aimed in97 p7 xm4pyo:xgosayw+ *1ti2v;rfw u-4pxjl order for the water to land with the greatest horizontal 1mwo* ;sfp xwoyv9pxr 7jay7:-+u t4x 2l pgi4range?

  An Olympic athlete throws a javelin at four different dey qrl*xz l+ (wm)ep/ /(8izsangles above the horizontal, each with th pmyq(+l/xze)*zdls/eri w( 8e 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 r t6,tu at be-iw;)5htfor the second time. If the ball leaves your hand with twice the vel t,)bih;uaew-rt5 tt6 ocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spr-u h8um bdyph7*t2) heed 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 does4+rcuc/bnx /p its speed compare to its initx4bncu p/ +c/rial speed?

  A stone is thrown horizontally from the top of a towerx(6.e)uxv xa8c wjmn6 at the same instant a ball is dropped vmnc .jw8(xxv a6eux) 6ertically. 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 droplqlcak71f q /wxvw3* +ped from the same height. Ignore air resistance. Compare the times of fall of the l/vc*1 xfqk3w a7qw+l two bullets.

  A plane flying horizontally at a speed of 66.7 m/s and at an elg (dk-fyvw+cg 12uw7djm+q/ t evation of 138 m drops a package. 6.4 seconds later it drops awyu m (1fdd++jq7 g/2g-twcvk 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 a secceo.k0l h9 *zuond package is dropped. Neglecting air resistance, the distance between the falling 9cekuo.lh*0z packages will

  A pilot drops a bomb from a plane flying horizontaloqa4ivch ;17 qbt2gp0d*wp9ely at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal pbhpgatei1; 4w2qdq0c 9vo7 *location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of th4pxno5hgm0f 1 r(j+ qwtz6x)h at on Earth. If you hit a baseball on the Moon with the same effort (and at the spe6oxh(nw0 4m +j5fphg z t1x)qred and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in th /nktdk/;69irn.ibdapm7 agie n4e7)e +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to /ndai k7e kdnpg ntae9;4) ./7ib6rmithe other car is

  You are trying to cross a river that flows da /e3) c wu00oi/cowwwue south with a strong current. You start out in your motorboat on the east bank desiring to we0 w 0o)/3iw/caowuc reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 kmi2 ;mqcfdo ;;e/h in still water. How much time will it take you to move 12 km downstreamcife;om;; d q2, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x a:cm45taqf+ if, fx.risr tv(0k) fhs7xis. The y component ofqvf7r0t hx.i4: )rf(mt ik+asfs5c,f A is

  If a ball is thrown with5en7dzi hl0). lxd70w*tcxf.be7 xvy 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 4-v2p2 tv ca ihvs4h-fline in a direction north of east and you end up 2.0 km north and several kilometers e c-tpi 2-2afvvh v4h4sast. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of z:to gq2byb3;its velocity is 8.00 m/s. The angle between the direction of its 3 :qtyo2 bgz;bmotion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a levele.vh,))q+lw9 x asar r ground. At what angle is the Sun el+avs ql. ,a)r 9r)xwheevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.t,q9a 2 cpvd77x)nwch5st1y i What are the components of the sum s2y5a, qxt niv c7p 1htd7)9wcof these two vectors?

  Two vectors A and B have componefp223cw2c m1nxfymg( .sh6 p qnts (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vec s1g2fm. pcy 3wpq2cmnx62hf(tors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the 0 sxm1s8jt s3axgl/.bo7qd: jmagnitude od ssbajot:xjxq0 s g/.m8l137 f C ?

  A car travels 20 km West, th)-vm0mrpkjx(; 26 akzb bv*,9gu dkyven 20 km South. What is the magnitude of its displacemkb k6yp2v9 gr,vxz u( v-*k);b0amdm jent?

  Three vectors, expressed in Cartesian coordinates, arv8ftm1a z .4m,qrx h;te
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,.ja+dxy5 2p b1 f 8kjzqh0hkm9 b/yp0n 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),cp6u l14vwrloirec 9 xon 85;)vycy ++ what is the magnitude of vector C = A - B lo; r4 +cc5 18w)xpyou n9l+vreivcy6?

  A runner runs halfway around a circu1e- zy/ x.(qr4*a6fnap i3o fs3vrxo jlar path of radius 10 m. What is the displacement of the jogge341vnia-zoes.6 f* yqx r/ 3 oxfrjp(ar?

  Two forces are acting on an object as shown in Fig. below. What is the mak+ exufzlvt(e a-iq a.f- 5k2,gnitude of the resulzu.,kk- t5-fv2eqeialf x+a (tant force?

  Two forces are acting on an object as shown i;xp 3d )hhnbo .b,)pzqn Fig. below. What is the direction of the resup ,xo q)zhb3)nb ;p.dhltant force?

  Vector A is 3.5 cm long and points alongn6z)*3jiyix oog 8 on+ the positive x axis. Vector B is 9.1 cm long and points at o *)n6gjo+zi y3x8ion$+57^{\circ}$ 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 long36tpjlggk.hv m90dx7 and points at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 38 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 16 m1yr5pc67eear 40r mo l/s from the edge of a cliff. A e ome 541r0yr6caprl 7stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 17 m/s, from k7niuz+b 4 ul2a bridge. It falls 17 m to the water below. How f72 b4unkiz+ular does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m 9,on*p92 hcc4 uf9kagf o7rl d9u k1odabove the ground, strikes the ground after travelin a9u * 7oru , o2glnkf9fdhc9oc1d4pk9g horizontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m// uec vczc04t( qzy(x/s at an angle of /zt 4(cq(eu0y vzx /cc$20^{\circ}$ 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 of 15 m/s at an x9b8ghza +i 39n+g mfa: 9h0vy)lmldld 5zlm3angle ofznbghm9+903a zi+5ha m:l98lyf dv)l3d lgm x $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an ysk7rnkxl j sw3;u3+1 initial velocity of 46.6 m/s at an angle of $23.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 556a ppis mam q17 s0fpc,csu4;:.4 m/s at an angle of $46.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at anglpg+ss 9*lgfs+ knyb yi 73q72/9tit 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 horizonewa3):5ulr0) :pfp lo i.oxel tally at 22.4 $m/s$ from the roof of a building 56.1 $m$ 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 in -+ xq 5f6ye5+ d0iu) qsload:97qwdj:jegcspitial speed of 66.6 m/s at an a 55:s0+g :dw oyel)jfx6+q aq de- cupqsd9i7jngle of $40.1^{\circ}$ 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 9ovz)uz -go 0 oaig0s*at a velocity of 4.0 m/s. If you ran the same race on azoi go*9)u0-sv0 agz o 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 osdg hp-f4h3;sf 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's s fh-;3dh s4gpspeed relative to the ground is

  A plane is flying duf**m4caauh5spv/ 4da e 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 120 kxac*e/ w/ k7f4,eqg hom/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 spee/7wf esygz /d/3qzlb g1kv n..d 50.0 m/s in a fo.ekgz/3f v/gn1y./wzdlq7s b rward 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 directedks+gxlc7-qba 0s 8yhjno)c 7; across a river with a current of 6.0 m/s. Wha as o78y7c-q)0 bnxc ;gkl+sjht is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in stillz. lfrw p4o(7se.b; rv water wishes to travel directly across a river 1.8 km wide in which thbs rpfz4.rv(ol w7 .;ee current flows at 7.3 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 tv :w71c/u. pgtvd ,cbzravel directly across a narrow strait in which the current flows at 5.0 m: 1cu/vt. dp, 7wcgzvb/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a riv9loic*n2b hfp/4c;l aer 200 m wide reaches the opposite bank in 6 min flo9p*bailn;2h/cc 4 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite 1cdk(xexy:r *bank in 6 min 40 s. She is swept downstream 480 m. Wh*x:dy rc k(x1eat is the speed of the current?

  A boat, whose speed in still water is 1.mzdb22thk:k h(b /sc298 m/s, must aim upstream at an angle of (c 2: th/ 2bdmzhkbks2$14.4^{\circ}$ (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)  $m/s$