Which one of the following is an example of a ve4tsrufcs v 63 tno4 ,lqy9y1r0 h3/qmwbn+6wnctor quantity?

  Which of the following operations will not change a vej 1fwnvu x2k1.7lf/kiv x5 n5qctor?

  Which of the following is an accurate stcjoltlcl6k5- 1,:.sof 6o7g;lzofq l 9p2grz atement?

  The resultant of two vectors is the smallest when the angle2puvlw2) ds c+ between them is

  Two displacement vectors have magnituddyx zhg04 6b pmcn 4alw0t:)i8es of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the sumy:i mp00xz wat8nc6 )h lg44bd

  Two vectors, of magn.ys+t:*1tne4wlr w y ;xn3jwpitudes 20 and 50, are added. Which one of the following is a possible answer for the magnitw; nw3 y.pjy4:er*tln+x1 swtude of the resultant?

  Three forces, each having a magnitude of 30 Ntn 5fh j-c 6p.mahxk9r-5g*y l, pull on an object in directions thaj6mach-.fx *9-5nrkyhtpl5gt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector rfb3r0c1d 1kx is

  Ignoring air resistance, the horizontal componeig4;.v;-+ucf -poav fyf t ua,nt of a projectile's velocity

  A ball is thrown with a velocity ofb0to nv:umuj+y+y3-j qn**q r 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 pr9ywgst twxfozml3+wm5 yz*7p2m t;.0ojectile's accelerationzwpl 0twz m9+2xw yg3st* .;75fom mty

  A soccer ball is kicked with .yb4xy-7m,nqdhf x. ck q2(ai a velocity 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 y5zm.x jxd.*)wtn /kwogy 5,e directed anti-parallel to the velocit.j5yxm), .tnwkwoed/zy5x * gy vector,

  If the acceleration of an objecze tso66,u- .oqdj:n2(yzxtph e0 ,avt is always directed perpendicular to its velocity,. j2 (zztphy6-aso: e0qnv, udo6xe,t

  At what angle should a water-gun am; * 7xqyu) -8gqssibbe aimed in order for the water to land with the greatest horizontal ranga-ub)mg issqy * 8;x7qe?

  An Olympic athlete throws a javelin at four different angles above t-yrdyx *5xq 2che horizontalq5-dr*x x2cyy, 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 j2jtua j1v/ r9for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal rantv ju9j2/1arjge R (compared to your first serve) would be

  A ball is thrown at a- ijb5/q de-tjn original 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 a*j6y ) 5hxsznt7,zj dcttempt reaches its maximum height, how does its speed compare to its ini)* y tsh65jjx7,ndzzc tial speed?

  A stone is thrown horizontally from the top of a tower at the same instant tio*yj2v dj7m 23et0 aa ball is dropped vertically. Which object is traveling faster when 7 dtm2 aviey t02*3jojit hits the level ground below?

  A bullet is fired horizontally, and at the same instant afm2*y16t7b5 tp:0cq lqd 3 njwzf ua1t second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of ttu 7q1 tcma3p*b16zq2 nf5:twy0f ljd he two bullets.

  A plane flying horizontally at a spm;d0,*n) +yc(vlez azt* bq pfeed of 109.8 m/s and at an elevation of 151 m drops a package. 6.2 seconds later it drops a second package. How far apart wiv +(ec),qalt0yzzpbd ;* mn*fll the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a sey93jo h 3:infacond package is dropped. Neglecting air resistance, the dist yai9fh :33jnoance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a-z:8q h /gipsa constant speed. Neglecg zhqa-isp :8/ting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only oney f5j58hekgmt- y4 1jg-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at54kg8hejg1yj tfm-5y the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h qth80ecliu*2 g ls4o q4ar,+ hin the +x axis relative to a straight, level road and pass a car traveligh82s,u4eh t r +cl*i4 0qqolang 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 av2x: 23v4e;o yk eauwn8fwtk, strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from you;k o y avtnu2,2eefv34x8:wkwr starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still w)qv)xiy) xai1 ater. How much time will it take you t a1xi)xqv))yio move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0o0/m ghue m t/o(dcg16 m at an angle of 30 degrees below the +x axis. The y compgo umg/e0/hm 6t(1od conent of A is

  If a ball is thrown with a velocity of 25 m/s at an an5tvc)7y gux( ya0 m*msgle 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 direction north of o2 o83qmm/ zny9 ow wmz*+vz:ieast and you end up 2.0 km north and several kilometers east. How many degrees oq8my+m9 2o:iwv/*omzn zw3znorth of east have you walked?

  A butterfly moves with a speedtvhkl/6o -do: ankucl7.s j1) of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direc)n7 ukst:l.av-ld/ c kjo h61otion of its motion and the x axis must be

  A 400-m tall tower casts a 6xxkb-+kzh9 8j00-m long shadow over a level ground. At what angle is the Sun elevated above 9 -b8k jk+hzxxthe horizon?

  Two vectors A and B have cbqir, fh2:4rb v0j cb)omponents (0, 1) and (-1, 3), respectively. What are the components)rbh0qjf v4ib : crb,2 of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), retbzkv ,0zohr,-nygx p 68 -b1espectively. What is magnitude of the sum of these tx-bn-o,hzp1g0k bvr te6 z y8,wo vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector 1uan; uk0 j/8fv ybj(iC = A + B . What is the magnitude ofj a0/1 i(8fnkj; yuuvb C ?

  A car travels 20 km West, then 20 km South. What is wc5zo4mgm q. 5) h7kbqthe magnitude of its displac45q kb7)q. 5mogzwh mcement?

  Three vectors, expressed in Cartesian coordinqz1p n6 jq7q9kates, 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 Cav.)mqln z+ j+0me+;s po-qjy artesian 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 vecto des40 v*1w rlhkc-.*kwq(sair B = (+3.0, -8.0), what is the magnitude of vector C = A - B wsv1 eqkac.rw4lhd0*(k*- si ?

  A runner runs halfway around a circular path of radius 10 m. What is the d-vgl g/dul.e0aq :d w,9z1m roisplacement of ta v- dwr,lgelg1q. 9d0o/mzu :he jogger?

  Two forces are acting on an object as shown in Fig. below. )o. o;/l/a wri-5zvyhevxncx3 lpt53 What is the magnitude of the resultant forpyr53v. lw5i/c/o-3t noa l zex;x)hvce?

  Two forces are acting on an object as shown in Fig. below. What is the direct0 oq8iyguto(x-q 73sx ion of the resulta8- qixyqu sgo3x 0(to7nt force?

  Vector A is 5.9 cm lal8pyds lkl(37d4) ,zwd 0yjhc j8pp7ong and points along the positive x axis. Vector B is 7.0 cm long and points ljcl y37 k)yd4 a0p(8spz8ddl7,phjw at $+53^{\circ}$ 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 63 cm long and pb/w u89 onsf8loints at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 35 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 horizon:isfkv;k78u2(upz n ltally with an initial speed of 15 m/s from the edge of a cliff. A stop si2k:;pn uz 7f(lvu8k watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, from a bridge. I ln4y2xzvle83tujvw/ 1(dpg9 t falls 19 m to the water below. How far does the rock travel horizontally before strie v/l(xu 1 4jtp 8gnvwl3dyz29king the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes th z jm9ym(mi.+at9o5zu e ground after trazi. j+ umytm9m5(z ao9veling horizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at anym2 ;b5jke 8cn angle ofj5 n28emyk b;c $20^{\circ}$ 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(x i(tf1c8a) tb8qrhl1 p4nrd a speed of 12 m/s at an angle (tiqdcnr h arl1tf)88b14( pxof $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 42.1c(t+ joex rtn*()*o6k 7ntwwh7d uj*h0p:qf a m/s at an angle of $12.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocikt w9,q;pk ct-afzp* 0ty of 28.8 m/s at an angle of $27.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired dxg9tb6,l zf- 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 horizontally at0z9rvbiq2 og 7 24.1 $m/s$ from the roof of a building 43.3 $m$ 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 grov ppiv0f)*e 3,nfy7sv bl g8z4und level with an initial speed of 41.1 m/s at an izyg nl,3vefvs p )840pvf*7bangle of $40.7^{\circ}$ 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 velocity of 4.0 mqzj sy,.u)c 1l/s. If you ran the same c,.)1sjlzyu q 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 duep+2kwfh rm1uye 23e 0)hn 4ibjh/ iat( North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the /4+ rfhai bewnhem)y(3hi 0tj k2 p2u1ground is

  A plane is flying du:g q3 y)2wotd*p/lldg7rs7 fke 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 spe nuk0ig-*e x9xw(9msoed 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 h 8f dfib:sdd073ovl3morizontally fires a projectile with speed 50.0 m/s in of3vd08lds7 i3fmbd: a forward 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 ae k 3mdwtf/ 9h9lle. sb24nwn/cross a river with a current of 6 f29knel/bdw 4lesn9 w mh/3t..0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/s in still water wishes toh,r *c3oui*pu-fu2 to travel directly across a river 0.9 k ,urofip*t3-u*c2 huo m wide in which the current flows at 4.1 m/s. How long will it take to cross the river?

  The driver of a motorboazxuu alc/ 7,j/v,x o1ot that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at x/,1a 7c xu,ulozj/ov 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading di; ackdr88;n) hvtc :swrectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreat8c; wav ksr8:)d;hcnm 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide b(: 1ut;ik0/ofqpzs b reaches the opposite bank in 6 min 40 s. She is swept down /qstk piuzbob0(;:1fstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.83 m/s, must aim upstream at ae(f* mv1grt0an angle ofrv etaf*1gm 0( $16.5^{\circ}$ (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)  $m/s$