Which one of the followingn++u1lr;8ripd ztrr 3 is an example of a vector quantity?

  Which of the following opef oc/h3it:5u q rbg8gb.ohwc-(7el*xawy+ -x rations will not change a vector?

  Which of the followingtnos2qe20 mhe g9 (vn; is an accurate statement?

  The resultant of two vectors is the smallest when the angl36n s*utmx b :*b0hwgre between them is

  Two displacement vectors hav*vcgemjv9bg n,b 0*; fe magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the su9*;fv0n*gebcg m ,j bvm

  Two vectors, of magnitudes 20 andh uo0gejn3r m9d8t slr+ 8;b9n 50, are added. Which one of the following is a possible answer for the magnitude of the resultandun8ro 99mh+t;jr8ns 3e lb g0t?

  Three forces, each h9r9amq z/px 9having a magnitude of 30 N, pull on an object in directions that are 9/aqz9p x mhr9$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownba7 ev7o e wh)t.ye+w4, the unknown vector is

  Ignoring air resistance, the horizontal component of a projectile'hgh fi40)l ;q ,k1rwnts velocity

  A ball is thrown with a vuil 7/( rzu2mtk.v /6iahl5suelocity 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 zh 5izni1k0l)component of a projectile's accelerationi)0zkiz n5h1l

  A soccer ball is kicked with a velocity oe8djjva7kj* ftn 2el iv1 o,38f 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 dirbau) -baux0 i,ected anti-parallel to the velocity vectuibu) a a-,x0bor,

  If the acceleration of an object is always directed perpendicular to it )fam,)a4miy,r oep d yvez+86fm,ky 0s velocit, 4y6ammkyi)pv,df)o a,f0rm e+zey8y,

  At what angle should a water-gun be aimed in order for the water to land kw2q+v nc 2wbawb6jw/8k*zx0,kt 6v ewith the awk 6x02wbk c vwzbje6,vk/nq*t28+w greatest horizontal range?

  An Olympic athlete throws a javelin at four:9* gx -edzxj1f 6,jczncnhck5 ah:7o different angles above the horizontal,9-:okdx cgc zxn* j,:fz1eacjhh n75 6 each 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 leaves yo l3:3692tg eipc xzxyuur hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first servet33cxu :p z2i 6gle9yx) would be

  A ball is thrown at an original speed of 8.0 m/s at a 4f+6xaintmgtzu e l60(m7 , nd+bmbv:n 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, +do0(ok3xz xcbmf+j1 how does its speed compare to its initial speedz+cf+0(xx ob j1ko dm3?

  A stone is thrown horizontally ,*ztpw3y: a8z6c8djm+s gkmefrom the top of a tower at the same instant a ball is dropped vertically. Which object is travelis:wa c y8kdjzmm8g+*e,36ptzng faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a wh/1/sn vc l3qr899skfrs :ue second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the t9 c 1/ses/f8:3uqhlw9kr snvrwo bullets.

  A plane flying horizontally at a speed oflo5gsio. l96vb:ovn - 9wu,lc 87.0 m/s and at an elevation of 138 m drops a pv9,i no:6lgulbloco v9 5s.-wackage. 5.6 seconds later it drops a 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 sex.nms3gj 4ll8o8u 1py/61tcl wok+ p tcond package is dropped. Neglecting air resistance, the distance between the falling packages x1s m1wgl4t8l+6p.uo 3olpn8 j c/tkywill

  A pilot drops a bomb from a plane flying horizon cxwk(t2:akm.(yg. v btally at a constant speed. Neglecting air resistance, when the boxv .(a2(bw. gkckm ty:mb hits the ground the horizontal location of the plane will

  The acceleration of gravityra;t1)w w. mv xh ,og6.qdqy ly,mp7s8 on the Moon is only one-sixth of that on Earth. If you hit as.rq8xl o .) vmp ;,wym1htgq7,6a wdy 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/h in the +x adptzecd w 8: 2* fw5*pb0t/xjcxis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the *0bepzw/*wcpt xd5 f82jt: cdother car is

  You are trying to cross a river thk 7v hw :c55kz4a(2eam4i pqa/wgfk;w at flows due south with a strong current. You start out in your motorboaa;g/c:k ivpzawmqw f a(44 k2k7w5eh5t on the east bank desiring 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 wat ic.r8cm +8ggjxi4 w9ver. How much time will it take you to move 12 km do gij.89mcvwc4rx i+ 8gwnstream, 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 q(j vb9rn75 uhr/r2piaxis. The y component of A isu2bv nq5 7j/irrph(9r

  If a ball is thrown with a velocity o8 n ce8wj(axqk,p 83z)tgs5rof 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 directw0no6cwka. 69qfh ol6ion north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east hlwk6 foaw hc06 9noq.6ave you walked?

  A butterfly moves with a speed acy(- 65xd- fk.mgxfoof 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x aoc5xxff --y.ak g (m6dxis must be

  A 400-m tall tower castsq).obt 2w qngkj192u d a 600-m long shadow over a level ground. At what angle is th t29k1ugbjo2nd q.w)qe Sun elevated above the horizon?

  Two vectors A and B hcwz)w1t(mu to y;3.;g,dik, ynct a1tave components (0, 1) and (-1, 3), respectively. What are the components of the sum of thesecti,1ydkam 3t nzty ;( wuw; )tg.co,1 two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3)hzgyyeys; ( vv 3r cssk4u:72., respectively. What is magnitude of the sum of these two vectrc.kz :gs ev y;y4v7s2h( us3yors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + Bq z :+b0f.(.qs var+nixx6x qr . What is the magnitude of (i+xs0xrbzq .6qrf qvx: n+.aC ?

  A car travels 20 km West, then 20 km South. What is the magnitude f-31l0.xps pe .ymcudof its displacem cfpes.1dp-3y0l mux .ent?

  Three vectors, expressed in Cartesian coordinates, enc-f odqan5*8vo: )1b ixy*xcx.6 dq 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, expressedk jty;: ;jhsn7 in Cartesian 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,. . qjnn4yzp,m l52fz7vqb zh/ml40bc -8.0), what is the magnitude of vec4bqf0n2z4/.b zcq .v pmnlhzy,7 lj5mtor C = A - B ?

  A runner runs halfway around a circular path of radius 10 .0q)ym u.p;l aqrqkg3m. What is the displacement of the jo ..agyruqlq;mqk0 p3)gger?

  Two forces are acting on an object as shown in Fig. below. What (5 jsehj +ou:y-t ypz.is the magnitude of t j:yyo5( -uz.tjs e+hphe resultant force?

  Two forces are acting on an object as shown in Fig. below.oxah9o;iz+w/39ak9rw 0so hg What is the direction ora 99hi3aoo0z/+ ;oxswgw 9 khf the resultant force?

  Vector A is 3.5 cm long and points along the posi 7;hbroa -aqip1h i4,u0b (k4binak5r tive x axis. Vector B is 8.4 cm long and points at-ha5poui,k1ra bq4 7ia kbr b4;h(ni0 $+58^{\circ}$ 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 85 cm long and points ayxmbhx f+db-.h2e d:p7/kgb:t $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 50 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 18 m/s from the edge of x m4.cf cnhl;og(:(zra cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.7 s. What is the height .fn:;zm gcr(ocl(4xh of the cliff?

  A girl throws a rock horizontally, with a velocity of 17 m/s, from a brifmu( zi qw60)vdge. It falls 27 m to the water below. How far does the rock travel horizontally before striking thvu(w6)0 qmi zfe water?

  A ball thrown horizontally from a pqr7mm xx 6v al3z*z7s,oint 20 m above the ground, strikes the ground after traveling horizontally a distance of 14 m. Wz*xs, r7qxmz 76mlav3ith what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speeq zost.f8 0rw-iqu4ix7f 29prd of 12 m/s at an angle of4f sq20iwq- roxpztiu9.8 r7 f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into t hhcdb/3*kh e6he jump with a speed of 12 m/s at an angle d*be6k/ hhh3cof $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 50.6 m/s at an angt9+ssj (pszx.ns bv1sex 17;yle of $42.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 21.9 m/s at y (+hbxjkg*/l7goyrglg1 4 8kan angle of $12.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedsu: f*7rj+:w 6ywk6aldj lsb) 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 horizohoe .f)wy8 db.ntally at 26.2 $m/s$ from the roof of a building 63.9 $m$ 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 l-xida) z,e nqhj5n0 u94ju un0evel with an initial speed of 64.8 m/s at an angle o0 hi5 uxd0 9, q4uzn)unjenja-f $44.3^{\circ}$ 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 veloc+o5 b7vb+lo kq, mhl7r 6cof(vity of 4.0 m/s. If you ran the 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 7lr loohv,7k6+m+ob q5cfbv (finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m1ra12s8(vz *) juqye yxipeo.tg ov 1*/s to the West. The plane's speed relatevq*o.z ge p*)81viou xyra(y11sj t2ive to the ground is

  A plane is flying due South/ p6mu40pw ymh ($270^{\circ}$) 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 head9qdo0yusstqft02 a2: z+whw6 ed $30.0^{\circ}$ 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 st-3c d g)y r0+cz*qtfm/s horizontally fires a projectile with speed 50.0 m/s in a forw yqcr30fgc+ tt ds)*-zard 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 sp c;ge02 gya6 icv//evtill water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses t;cgep v/g ya 0/v2ec6ihe river?

  The driver of a motorboat that can move at 9 m/61 ku9auz7xtzs in still water wishes to travel61uk7z9t axu z directly across a river 1.8 km wide in which the current flows at 5.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/gte+o/ ed8/us7l6qqx s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m q6 gte7l/seox8q/du+/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the 8l00l xfq8 ujfopposite bank in 6 min 40 s. She is swept downstrj8xlq0f ful8 0eam 480 m. How fast can she swim in still water?

  A swimmer heading directly acrosro *(xyeh6m8p s a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speedr6e8y( ph*oxm of the current?

  A boat, whose speed in still water is 1.87 m/s, must aim upstream dyal .5ilbn+; at an angle of dn;ia5.l+lyb $21.5^{\circ}$ (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)  $m/s$