Which one of the following is an example of a a;x,x cemx.+ ivector quantity?

  Which of the following operations 4,bu p2.oe4yaj ukpg5 will not change a vector?

  Which of the following is an a8sas1c0 sb u (pp:ozzu.d2hl1ccurate statement?

  The resultant of two vectors is the smallest when the angle between th-g-r/abh6lewb; x z e.em is

  Two displacement vectors have magnitudes of 5.sl9 xf p0q4*cy0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of 4l f90p cyqx*sthe sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followmv5dfj01st+qc,ty5y q jv ,y1 ing is a possible answer for the magv,1jcqyyq+1 my 055djvsft,t nitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direcva q0)n* .+ saz1ljugotions that sqa+j0 v.l oa)gu*n1zare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector (8u0 /xnh*4cns6lm zdf-pp fdis

  Ignoring air resistance, the horizontal compcu j(;rwh.+ fz54muten 0ma8 ponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an hoi +b +yf8h9 ,9 ;3zjiydofruangle 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 accele-wgrb* zhu5k+,hya fk,fa,z /ration u,af,hkhr *fg-5akz, wby+/z

  A soccer ball is kicked with a velocity of 25 b:w xe+5c2 be6sgrh(p 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 anwgfca(1 nmh pwo:z. 98ti-parallel to the velocity vch981z(nm: powfwa .gector,

  If the acceleration of an object is always directed perpend+hg ousv9-,p9pxq1sf m2gld3sm gr 4 a+f),bdicular to its velocit+d fv mlf + 9op 2bsugd)xs9 gar,hq3sgm41,-py,

  At what angle should a water-gun be aimed in order for the water to land scedfc8ite2o hwd*h65b4n0, dofxjq*n,+e5with the gre6,ddwt c42feofen qho+*b0dx5 , 5hs*c8jineatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horib r3rm351iy 4avm/l0lf*xu 6eb z,egdzontaxer,lir 43l/b0gabm6 u fz d5v1e*3my l, 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 t313+elhqbk.b qvxu )m0hoq ,yime. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal ra3) bh+kexu b.1yq3vqm0ol,qhnge R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 cv*f1 1o(5bf 0mfje jlm/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 go:5tyao x47v agal attempt reaches its maximum height, how does its spee5:x4agot vya 7d compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a bad+tz129(ns(e 5ogcw+my cg dl ll is dropped vertically. Whiy+mc dc9(t(12eos ndlz 5w +ggch object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant azpwpg(+89t 4 ,r,k)tiwf mdef second bullet is dropped from the same height. Ignore air resi)z ptgfi(49wmd+,8wrpef ,kt stance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 67.7 m/s and at an eleva ,0ehte rydy*.tion of 248 m drops a package. 2.9 seconds later it drops a second package. How far apart will the two packages land on thhdt.0 yye, r*ee ground?

  A package of supplies is dropped from +x kh g5 (m27 vcd.fd4ecekw7aa plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fallifa5.kg4dk 7e2(mccxd wevh+ 7ng packages will

  A pilot drops a bomb from a plane flying horizontalz 53xe(oy3ktd1cuauw8 i; 6jiml uw:3ly at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal(35;3lix uauie63mt1: ouwwj8zcyk d location of the plane will

  The acceleration of gravity onqt o4 08p,dd+mgyy 7cn the Moon is only 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 woulycp,m4dd0t y7 8ngqo +d land

  You are traveling at 55 mi/h in the +x axis relative to a straighto:undvqm7 6 svf 6rumi8 +m81l, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the ot+86 u f8 omv mvmsu:67qnr1idlher car is

  You are trying to cross a river that flow5a+);cbb*vt zzdc7 . z3im3hzci ;hz hs due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shz b i;hczt z. 5z7b)di*zch3hacm+3v; ould head your motorboat

  Your motorboat can move ;r un. zzuf,3kat 30 km/h in still water. How much time will it take you to move 12n f u3,z.rz;ku km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrmh qdx01c /)qm)g+ hzzees below the +x axis. The y compongdqh1+ /h x0mzqz)cm) ent of A is

  If a ball is thrown with a velocity of 25 m/s at kw up gpa3pn fa0bv +c9a2y(ie3+j u;;an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straighs6zdvf/ a2.dorjbm;j4) g0fp t line in a direction north of east and you end up4j;)6 0fzfjdvasmg.db2or / p 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 1yvlhz6435bab ufx 5- epzxayh 3k43)q2.0 m/s. The x component of its velocity is 8.00 m/s. The qa5vf46yxe) p4 3l xzh3byk35u h-zabangle between the direction of its motion and the x axis must be

  A 400-m tall tower castsrwu(+;0 .*qaxrf,m2w klwq ob a 600-m long shadow over a level ground. At what angle is the Sun elevaw *. mxq;uklwa(bo r, 2rwfq+0ted above the horizon?

  Two vectors A and B have components (0, 1c3d) -2k x d vfv;v rrs25qv:fiwz)b:d) and (-1, 3), respectively. What arebr::dvsv x3vv2)q)z2dri-f ;w d5cf k the components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), r/q7-0wm sbh-c; ggfkwespectively. What is magnitude 07/wkg m; swh-g-bqfcof the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B pn)p.x (5radp . What is the magnitude of C x 5n)prap(.dp ?

  A car travels 20 km West, then 20 km South. What is the magnitdr3 y)c0g5;ieg /dzkl ude of its displac ed;0z/ lyk5g3)dr cigement?

  Three vectors, expressed z*s9cg pdc p:)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, exprefm rvcg.-wu++tcwa3 -ssed 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 ve1v qo2a mo///-s nptl2d 6ejud 6if 5lhzn67pictor B = (+3.0, -8.0), what is the magnitude of vector C = A -pfljvu/6st6a m/h1z/iod7qd52np6o n2 le i- B ?

  A runner runs halfway around a circular pa lmmbo2 dmg(1;/.(hn7 bmi*uau cuz ,bth of radius 10 m. What is the displacement of the joggemd*m/( abbnuco g;u uz1b 7,.lh2m( mir?

  Two forces are acting on z x2sug9(6tcpan object as shown in Fig. below. What is the magnitude of the r629xpuzg ct(sesultant force?

  Two forces are acting on an object as shown in Fig. t 3rz1n ekcf mc rdt+7u,mp,:nj564aabelow. What is the direction of the resultant, c6n+:raetjt3 4,mkf z51umacdn 7pr force?

  Vector A is 5.5 cm long and points along the pos(;d br4umq5 q -9kfw5 kt:y 5blqw9wheitive x axis. Vector B is 7.5 cm btfwkqw mydq5r 4(l 9;5b5uw k:h9-qe long and points at $+59^{\circ}$ 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 89 cm long and points afq vnu(5z /7t 7zik+u rji)jw,t $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 43 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 30 m/alk. j /p :q 7tj;30ugsb6ujnfphqta4/m1+ mh s from the edge of a cliff. A stogqtu/. :hjk 1tq pa+h;7/paj40bj6snum3mf lp watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.7 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 16 m/s, from a tw 18qpcar )ifhi8 wsj (5:6wtbridge. It falls 19 m to tjq1whsfc5r8 piit) 6: w(8 awthe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 m abovec0w6 xd.6l bvj zotpk k)-yjv8yk8b33 the ground, strikes the ground after traveling horizontally a distance of 16 m. With what speed was it throwj0bxpvol)j c6 8 .3zd-ytkkb vkw683yn?

  A jumper in the long-jump goe4:g tl:4c/8nlym5hs nb) q eruixoi.9s into the jump with a speed of 12 m/s at an angle og u s: lox m:i5)nnrqcy48.l4/ 9ebithf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long6r-qpj-d-k y7p4 85b zod ysrw-jump goes into the jump with a speed of 13 m/s at an angle ofpk-qd 4-j y-dybs7 oz5 pw86rr $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 45.4 m/ju, b2* t/yis -ow7 m2v7mahwbz8(tgrs at an angle of $48.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 31.3 m/s at an angl- bdv;e+a8pey e of $42.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglewf f2ueno1g wc9 f*,7h 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 horizontaqxow ;64ot +p fq2)x*db4nh xilly at 24.9 $m/s$ from the roof of a building 54.3 $m$ 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 5 vk(54bntti r8wa)qwxfx54 ;d 5.0 m/s at an angle xfkawx45tt vb)i wq(4dr5n;8of $42.7^{\circ}$ 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 velocitcspv,(oktuwp3 oo5- : o*dk.fi8f3 oxy 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 c.po-8o * od:k5t iwsxpv3(fkoo,fu3time it would take you to finish would be

  A plane has an air speedgidmk(,7yc9 i of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground ic9(y g,md ki7is

  A plane is flying due S4fxszej -cd ,3outh ($270^{\circ}$) 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 spe ab;n( ic-wbr3*e/vroed of 120 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 htkyc zvb: b)7bvw)( w9orizontally fires a projectile with speed 50.0 m/s in a forw9)tzc7w vwby b:bk()vard 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 irnf8-x+)ev wzs 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the spe zr+fxw8nv-)eed of the boat as it crosses the river?

  The driver of a motorboat that c ui)1dc)ekqb jq5 hl+gr88a2zan move at 15 m/s in still water wishes to travel directly across a river 0.6 km wide in which the current flows at 6.3 m/s. How long wij 2+858 he gkb) ruqd1zla)cqill it take to cross the river?

  The driver of a motorboat that can move at 10 dci.x/j 88ume m/s in still water wishes to travel directly across a narrow strait in which the currj8.ecdu /mxi8 ent flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acre tg)0)s, akn 1rs+eg :yg2vdsoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is:e,ya1dg s)rsk+ne 2sgv0tg ) swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide ieprb.qrdt(+9*xou-4s7w )lr3tzxqwjz3 1b reaches the opposite bank in 6 min pxwo) q7rl(zj 3ib*r be zt+twuxq 1943rd .-s40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.37 m/s, must aim upsto wvn2w*u;x;06tiav bream at an angle of a2o0x*n ;6 v b;wivutw$19.3^{\circ}$ (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)  $m/s$