Which one of the following is an example of a vector0lbn.;e7 (3 lzbi ajlj)r0 fiz5l+ lhm quantity?

  Which of the following operationtq)4nk l/fio no,sc59riu(8 z s will not change a vector?

  Which of the following is an aa)tu g0 spso2*ccurate statement?

  The resultant of two vectors is the smallest when th)e5yo zn c)y37-qeosje angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respect mf0k/,ju rp3vively. When these two vectors are added, the magnitude of the s3upjf/rk0 ,v mum

  Two vectors, of magnitudes 20 and 50, areds uajl yrx 2::pa277;dq;a zkorl37 p added. Which one of the following is a possible answer d p7p2 orja:7 s23zlx uy ;raq;la:kd7for the magnitude of the resultant?

  Three forces, each having a magnitq px:mp)tki xzz18v .9ude of 30 N, pull on an object in directions thazmqp:k.xt x8 pvi )z19t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecyp f2nuk9y3 wo6 s+jg*h7sf g:tor is

  Ignoring air resistance, the horizontal component of a projecti uu r5 / rgd4djpwd91ea)btj-(le's velocity

  A ball is thrown with a velocity of 20 g3v3 7,vhra)o fkk c::khc ot;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 hor6bg;pm.vm,a4-kxzd xizontal component of a projectile's acceleration, m 4-xa;gbmv6 kpzxd.

  A soccer ball is kicked with a velocity opth *.pei6dp a dnxp) d(d7cnqk+ /.1tf 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 ooml: h4sc0z 9e.1ee.hh8mhs if an object is directed anti-parallel to the velocity vece 8hehs4:olm. ei. s1 9h0hmzctor,

  If the acceleration of an nibp (/ugi) b*b;rhh 9object is always directed perpendicular to its velocity*9p ibuhi()bnbrh /;g ,

  At what angle should a water-gun be aimed in order for the water to land wif6ff,s30rh uzfs5z ( fth the gfusz0 6s3 fffr,(zf 5hreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above tyg8gi+b**,qfarl 6p.w2m zjj he horizontal, each with the same 8 jgmry6* z+j .*g 2aiql,pwfbspeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. tmwv *64rftghceg ;cs34u97y d:pr,oe k1v 1t If the ball leaves your hand with twice the velocity it had on you f1:ev uogcrg 3 749p*yttch twm6kv4es,d1r;r first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle osxn;w0wy1c5 g f $35^{\circ}$ 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 reachutteh 43e9+nbes its maximum height, how does its speed compare to its init 43btu ene+ht9ial speed?

  A stone is thrown horizontally from the top of a tower atx4u8 e5v3 j/ qiwlqp*t the same instant a ball is dropped vertically. Which obj8twxjel q*34q5vuip / ect is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bul4vi+)t gslyz rs;:j5mlet is dropped frt+s)ij gzv;yl r:m54som the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 112.)sra sa5df 4fpeqwfur6qv-s59+,o+o 5 m/s and at an elevation of 218 m drops a package. 4.7 seconds later it drops a seconu )e,65qr spo+f- wf9ado a5 q4rv+ssfd package. How far apart will the two packages land on the ground?

  A package of suppliedxp*pde. +8bodse 3x5 s is dropped from a plane, and one second later a second package is dropped. Neglecting a d xe+.xsbed8*pod5p3ir resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. e 9 ,b)mjeq-phi+uotcu :-ig ; Neglecting air resistance, when the bomb hits the groun e,q -iut;bcohu g9i -:pmej+)d the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Ea9pg8oyal yxqj1 )4c yq/e2 o3zrth. If you hit a baseball on the Moon with the same effort (and at the speed anzp/j 3a 1xgq2y 8cq4ooy el9y)d angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a awr4; qls+:ueeqqgu;yh j.- -straight, level road and pass a car traveling at 45 mi/h. The relative velocit;ya ge .qu4j-u qs qhlre:;+-wy of your car to the other car is

  You are trying to cross a river that flor1+ oo9eo0b-u 2 wxkek p)wj8iws 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. 92) p8-o wew 1jeoxik0 korub+You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time of23ja5xvyxrt zk1f h,.e f..will it take you to move 12 km downstream, in a river flowing atzvkef5 2.xh. a. tr,jo1ff3x y 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 dwfk 9k f;9h tzjc*y96phz b:fd.v.x*iegrees below the +x axis. The y component of A ix9phz:.fk6vihffw yb9 *z.*j ckt9;d s

  If a ball is thrown with a velocity of ffq j+d-e,, hm 3 uv*eer0 n3ch8nt)zs25 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 iwn +bxjjd,s x1dq6 ;w r3s+dk(n a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you walked?jw,x+s3w ;k1d r+s6bd xnq(d j

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is -d) q+v7guhurn;k2 zj8.00 m/s. The angledk 7 gzqu;uj2+n h)-rv between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level growse*he6nk0 0c :rkw 6nw.9rvsund. At what angle is the Sun eleva6n0 v*9w0es:w6krne.w rhcsk ted above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respec mh xksv81.t(s. cn3gstively. What are the components of the sum of these1gkx t(mn s.hc. vs8s3 two vectors?

  Two vectors A and B have components- :rqbb- mf3ro (0, 1) and (-1, 3), respectively. What is br--f3bm:o rqmagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C =7krp aj2-ljje2ql:+*v9ewn2 h(yf ca A + B . What is the magnitude awjqe9e2a lkp+fj2j*hv 7y: rl (-2cn of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disp- i7lfj,e5vg mlacemengmj7vfe-,5i lt?

  Three vectors, expressed in ebwqn48 5,mzrtb 3+dpCartesian 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 Cartesi88ca catqmd1: an 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, -8.0), qipyi(l5kz;; what is the magnitude of vector C k 5y;z(iliq ;p= A - B ?

  A runner runs halfway around a circular p fsch nq7/:vl5ath of radius 10 m. What is the displacement oq vn s5fc/hl:7f the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitudf 1* :4cv xgrs3qvnv**tvrzs5 e v5vgcq*fx :zr 3* *sr1s4vtnvof the resultant force?

  Two forces are acting on an object 7oxvz0i8m),z irvxx )y/ t8ady /hxn5as shown in Fig. below. What is the direction of the resultant force?8yrha )z) x x0xn xv5//7vmioz,iy8td

  Vector A is 4.9 cm long and points along the8ru -g.7a:tjm oxh/,t7f j ghv positive x axis. Vector B is 6.2 cm long and po / .h7hujjgo fav87g:t-m,t xrints at $+58^{\circ}$ 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 52 cm long and pointtzs-bz 8*b6fbv rvr6)i *td6ws at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 26 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 10fp5ohl mn x . pqq7)v.:1ggt*t+v)nzi m/s from the edge of a cliff. A stop watch measures the stone's trajectory7p.:x*nvi)mno f lz.+ qpt5gqv)gth 1 time from the top of the cliff to the bottom to be 2.1 s. What is the height of the cliff?

  A girl throws a rock horiz t:a4 *6tm9hi4tgzilyontally, with a velocity of 15 m/s, from a bridge. It falls 21 m to the water below. How far does the rock travel horizontally before striking tht*i4:g zti4m 6y laht9e water?

  A ball thrown horizontally from a c)q ic r/h4xo8point 20 m above the ground, strikes the ground after traveling ho48cq)h rx /ciorizontally 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 an angle1trhjscl-oj : 6j h-.s o. j-jsrst:h-jl1h6c of $20^{\circ}$ 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 wit+ gnek kl*yrxr(lg:9kys58) rh a speed of 13 m/s at an angle ry:g8kxkng(krl l 9*+ 5 )esyrof $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitkw1,-asb l n99wudw-q g 1nl.ey of 26.1 m/s at an angle of $45.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initiarahg3 i * tryw/us5a. ,7,ybgxl velocity of 40.5 m/s at an angle of $35.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at iihk 3lc3;k* dd+w l0san 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 at t-;/ ( dqprqfb: n*tfh 26.6 $m/s$ from the roof of a building 40.4 $m$ 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 o7pw 0ao 4 -disxbwx43ajt v/u9i;h9ctf 45.3 m/s at an angle oci-bha 7a soxp wtxj9d43ui094;v t/ wf $38.8^{\circ}$ 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 1k23 inb 4q0ngd500-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, the time it would take you t20niqng3dk b 4o finish would be

  A plane has an air speed of v,by ,b;ntt;wqrvo: ;d82 uhj 200 m/s due North, and is in a wind of 50.0 m/s to the West. r;d;u 8t;hn q bwj bt,:vo,yv2The plane's speed relative to the ground is

  A plane is flying due South e4xw p *v 7n(, dzxhjvy2ia/4v($270^{\circ}$) 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 mhg .x 1i5b(uskdp 0j+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 508sf( h6jfl pui2k/)xn.0 m/s in a forward directi l8fhf/kp s6 2i(nx)ujon $30.0^{\circ}$ 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 direcw)ax:yt6l w iwkr0 9fh *a*zw1ted across a river with a current of 6.0 m/s. W:riyw6*0tkhw 1* xwwafl9a z) hat 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 wishefm; u 8dgch25l.3ppqks to travel directly acr3g2c5khp ldu;pf. 8mqoss a river 0.6 km wide in which the current flows at 4.8 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s ii0utv0fi3 m6 cn still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what an6 0 uf03ictivmgle upstream should the driver head the boat?

  A swimmer heading directly ac- qt*5sxr. xp3cpi,z wross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept do pcr s.xxz- pi3qtw*,5wnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposclmn6 /p: rt2+auaq4i1ipr0p ite bank in 6 min 40 s. She is swncqr:up tiilp4+ r1 0maa2p6/ept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.17tqo iav)civ;b,. e ,k0 m/s, must aim upstream at an angle ofi0) bvt ecv.,i,qko a; $25.1^{\circ}$ (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)  $m/s$