Which one of the following is an example of a vector quantito*utq.ejv7 ee9x0c k1 u2;yvfy?

  Which of the following operations will not o23rz k/om5l ct sk zaj7)sq+2change a vector?

  Which of the following is an accurate f. 4y 3ksd,a vtinaa*6statement?

  The resultant of two vectors is the smallest when the angle bo ch,qb:3d 2daetween them is

  Two displacement vectors have magnitudes of 5.0 m and 7rcmmx 01h/u8- q1oa nr.0 m, respectively. When these two vectors are addeq1a- nxu1 8mr m0/hrocd, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, qj3 tm.z+cs +care added. Which one of the following is a possible answer fo c.cz+jm3st+qr the magnitude of the resultant?

  Three forces, each having a mahg et *)il0/uv2 x9c-jyd3veggnitude of 30 N, pull on an object in directions thad ey*x-chu)32 itj9lv/v0 eggt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecwa 9 ;l+z6t. jf:kqpsntor is

  Ignoring air resistance, the horizontal component of a projectile's velof):q,y;*7 frk vcj59fiiiu nycity

  A ball is thrown with a velocity of 20 m/s at 8pj4nl t5w ui;i.n z;iaf*3g qan 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 proc: 9rq27(- d*40jw, vjbl cwfijic grxjectile's accelerationc27 w*0rlxc i-jbj9rgw f(v4,i qd:cj

  A soccer ball is kicked we7uj3zxhmr u)7 *sa)eith 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 directed anti-parallel to the velocyh8 )k*fd 5: n sb*1uu3kvh nbcnbl1t,ity vector,cbkh)htk3luu81yfb d *vn:,ns5b*n1

  If the acceleration of an object is always directed perpendicular to its velw6f5eoz5 o72*s m keryocit525*roweezs yk6f 7moy,

  At what angle should a water-gun b+qifk8 .c,7ztvdk/msr t) rr(khq , q9e aimed in order for the water to land with the greatest horizontal rangqs,k)/md.7tv9r+(z kfq hir k8 ,qtcre?

  An Olympic athlete throws a javelin at four different a n3 a rh-cn3ggat9al+ .tr73gfngles above the horizontal, each with the same speegnn3+h .g l-r c3 a9rf7gtaa3td: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 your hand wity3pfohlqy1x3jc 3 g8c()f1pbep5t6 z h twice the velocity it had on your first throw,18z1 xlb)ft 6f(epc pc3 qo5y3hpygj3 its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0fffjf b/3ts4vgntu6b4;5e k/ 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 goalg: ig2kfkpgs3q4e, t: attempt reaches its maximum height, how does its speed compare to its initial speedk3g :q4pftski: g g,2e?

  A stone is thrown horizontally from the top of a tower at the same instr,o8/;gccm d qant a ball is dropped verticallo/m; d,8gcq cry. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the sam : )aghs4inw;3 7jj6axb1bmkge instant a second bullet is dropped from the same height. Ignorexhb:wgna4 g1m6 s7 )jbik;aj3 air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontbw3jsf(b.gh,m3m v1 /eci8m:rsu (d zally at a speed of 90.0 m/s and at an elevation of 144 m drops a package. 3.2 i3sb8h s/ .(jr3( vd,mf1e:mw bgcmzu 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 play4 la*h)x l )s kz0z*yj*x9kbnne, and one second later a second package is dropped. Neglecting air resistance, the distance bexy ly zs)zbkh0ln49axj**k)*tween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a consta bwzke+*6 acic s3+uh2nt speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wi++6 we 3bk*c husza2icll

  The acceleration of gravity on the Moon is only one-sixth of that on lb s2b,; : o2imrt7g nnock-*fEarth. If you hit a baseball on the M o2cbt -2li rb,7:g*;nfns mokoon 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 ujn45z z*6 j ycdqdg(:axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car q: d ncg4y6(zzj*j5du to the other car is

  You are trying to cross a river that rmjwhfr d: 2nqimzcl) u3y6-m 6(p 82dflows 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 poi3-qwcdipyf mrd : m2u(j62 6zmnlr8h)nt. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much ti6ztswn0n:j sw9t0/ hy me will it take you to move 12 km downstream, in t0 0 yssw /nw9n6jt:hza river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m+y4bbqoai e27ti k2;a at an angle of 30 degrees below the +x axis. The y compa2+yieab ;7tqb4o2k ionent of A is

  If a ball is thrown with a velocity of 25 m6 +wekd3wgf q)s8 zc;l/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 s*4ty7.bnukv:.brf vh2a b7zin a direction north of east and you end up 2.0 km north and sevekra7 t vbvnbhz4:. 2uf*s. yb7ral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component o)j+jma ix-d3 ov4c -exf its velocity is 8.00 m/s. The angle between the direction of its moedcjj4-aiox+v) xm3-tion and the x axis must be

  A 400-m tall tower casts a 600-m longk (fk .i2dvkz ;iz9ty9 shadow over a level ground. At what angle is the Sun elevated above the horikz9d(.z9itk2; viyf kzon?

  Two vectors A and B have components (0, 1/)8yj.hvrwt.k j* 3l b4m xjpt) and (-1, 3), respectively. What are the components of the sum of these two vectorsp t.kj.*/jht8) brjvx4 y mwl3?

  Two vectors A and B have x13w9ilcf8 nrcomponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two 8r9 3fl1nwxcivectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitu3 2d*h6 8*fbpbjboiq m2v;bhvqln8,jo v 84onddnbfbo*iq;63q j v8v8ljvo*8nh b, 2o4bm2hpe of C ?

  A car travels 20 km West,)y( 4mp6 e/xqknz sytc,w/za4 then 20 km South. What is the magnitude of its displacementmkzen/y4aqs)w,z c4/px t(6y?

  Three vectors, expressed in Cart zj2l.0hn 7nco7uklwz 6ike4 6esian 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, expressed in Cartesian coordinat7fvr3z6k-om9v- gpwo es, 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 vect xu ,kf f-1ighx3h2nc+v6+ lftor B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?ltfic -x,k+x1ff n+6 hh2v3ug

  A runner runs halfway aroun, v14gznmqdv b 5:ok(n9kuba(d a circular path of radius 10 m. What is the displacement of the 1,(9(dnkkub:vm v oaq4gnz5b jogger?

  Two forces are acting onw o2ux+ h2p99vwh/n *ami,bvl an object as shown in Fig. below. What is the magnitude of theu m+*2h2w9vbvlh,/wnxia9 op resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the direczq 6ouxj h29yt e7w:np i 13;fkdl1y8ption of the resultaz eho:7jp ;x9 1tiyfud1ylqp2w8 3nk 6nt force?

  Vector A is 5.3 cm long and points *ji5iw v*n. bialong the positive x axis. Vector B is 7.7 cm i.iwin5vj* * blong and points at $+35^{\circ}$ 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 61 cm long and po8b +aq ui0g/cm:en1xm ints at $30^{\circ}$ above the positive x axis. Vector B is 28 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 horizontally with an initial speed oft./(rtqmpfh6ut :bzt)b us 4 p(1ud5w 16 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 4.1 s.q tubtru)h bt fmts:p.5p6/ 4d1z( (wu What is the height of the cliff?

  A girl throws a rock horizontally, xbmq: i t5ynr 90r-w-kwith a velocity of 11 m/s, from a bridge. It falls 18 m to the water below. How far does the rock travel horizontally bemnxir-y 5:w-0r9bk tqfore striking the water?

  A ball thrown horizonf 2nhpf qz8+w)4u2jdo m02 rcftally from a point 29 m above the ground, strikes the ground after traveling horizontally a distance of jff8pzfo c dnmw)hu r02422+q 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spe7d 3r (kai88k)vtb zj-z8xpm bed of 12 m/s at an angle of 88t(b3a7ji)bzz-xk kpmr 8vd $20^{\circ}$ 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 10 m/va 25h,o2*f wki9ga h/*nj pnyb6yq6us at an angle ojgynhiq 2*yk *, 965 paw6bafuv2oh /nf $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched rdjg;4cpf-lopn62 9t with an initial velocity of 37.5 m/s at an angle of $11.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with abh wo 0my+r4t7wlzm1f;ni tx*i) gt.7 n initial velocity of 59.5 m/s at an angle of $35.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fir 9- n.lkevx(fu5e *svied 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 horizontally5)iy-jic4r su+iv-y p +fyh5r at 26.4 $m/s$ from the roof of a building 58.2 $m$ 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 froq qlm u wu;y:*zlh3+2bm ground level with an initial speed of 43.5 m/s at an u;mqw2bq h :y*z +l3ulangle of $47.7^{\circ}$ 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), yo,nnd5sc4 m. o2ce 9/eoi psp6ou can run a 1500-m race at a velocity 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,ip5o ,9do/6 p4sns2 cne.moce the time it would take you to finish would be

  A plane has an air speed ounnv)j v -/h x)r71mcbf 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed jcvh7bx) 1n )m r/-nvurelative to the ground is

  A plane is flying duqlveaau/d0ia49c s cql91o5 g9.a ; zne 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 120fr g-t7up4btysv8*)b dp- 3lxn53 ohr 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 horizontally fires a projectile with speed 50.jxt;77rbk8 h wy ;cj6f0 m/s in a forward d7;8 b6tyw j7fjx;kr hcirection $30.0^{\circ}$ 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 8.2uu yp6 3-nbrs0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of t 2nr3 pu-yb6ushe boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes tq,frae ; hhu0(o travel directly across ea ;huqrh ,(0fa river 1.4 km wide in which the current flows at 6.5 m/s. How long will it take to cross the river?

  The driver of a motorboat thad.c/jy+bd /l:ht l3g ngy x(-lt can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At h 3+ lgljl (d.byn/d/t xcy:g-what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the )w cs):qodf2n okz7r4opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in sti72fsco rz:4kn do)qw)ll water?

  A swimmer heading directly across a river 200 m wide reaches the opposite ban hd i9-c6nz+ufx (47kemk4h wsk in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current-s4+ xc9(6m ehfn z7kk4whdui?

  A boat, whose speed in still water is 1.70 m/s, must aim upm9* 3myxcy3pa db x3*ag4z5ywstream at an angle of m*az*ymyc5b w34xg p3da 9yx3 $27.7^{\circ}$ (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)  $m/s$