Kinematics Type 1

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STUDY PACKAGE Subject : PHYSICS

Topic : KINEMATICS KINEMATICS Available Available Online : www www.MathsBySuhag.com

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Index 1. Theory 2. Short Revision 3. Exercise (Ex. 1 + 5 = 6) 4. Assertion & Reason 5. Que. from Compt. Exams 6. 39 Yrs. Que. from IIT-JEE(Advanced) 7. 15 Yrs. Que. from AIEEE (JEE Main)

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THINGS TO REMEMBER :

v2 v= ; a= = v ; s = v d t ; v = a d t ; 2 where the symbols have their usual meaning . ds dt

dv dt

dv ds

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The equations equa tions of motion for a body moving in in straight line with unif uniform orm acceleration, accelerat ion, are (i)

v = u + at

(ii)

a t2 a t2  u  v   vt  t  ut  s=    2 2 2

(iii)

v² = u² + 2 as

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. 1 8 v u 1 8 t (iv) sn = u + a (2 n - 1) (v) S= 8 2 2 5 0 If a body is is thrown thro wn vertically vert ically up with a velocity u in the unifor uniform m gravitational gravitatio nal field field then (neglecting (neglect ing air 3 9 8 9 resistance) : 2 0 u u (i) Maximum height attained H = (ii) Time of ascent = time of descent = , 2g g 9 7 2u (iii) Total time of flight (iv) Velocity of fall flight = fall at the poin po intt of o f projection = u downwards downwar ds 7 7 g 3 0 9 KINEMATIC GR GRAPH : 3 Slope of the displacement time graph at any particular time gives the magnitude of the instantaneous 0 9 0 velocity at that particular time . : Slope of the vv - t graph grap h will will give give the magnitude of the instantaneous acceleration. acc eleration. e n o The area between the v - t graph , the time axis and the ordinates erected at the h P beginni beginning ng & end of time interval interval considered will will represent represent the total dis displa placeme cement nt of the body. body. l a p RELATIVE VE VELOCITY : o h (a) Velocity eloc ity of o f ‘A’ ‘A’ relative rela tive to t o ‘B’ is given by VAB VA VB . B , ) r i t o the velocity veloc ity which ‘A’ ‘A’ appears appear s to have as seen by B. The above abo ve idea of 1 VAB refers to S . dimensional dimensional relative motion can be extended extend ed to motion in 2 dimensions. dimensions. K . (b) (b) Angular velocity of A relative to B i.e. AB is given by R . S ( velocityof A relativeto Bin a direction perpendicu lar to AB = a AB y AB i r a K LEVEL GROUND PROJEC JECTILE MOT MOTION : . When a body is thrown obliquely (in a vertical plane) plane) into the t he uniform uniform gravitational gra vitational field field then the trajectory traject ory R g a (actual path of motion) motion) is a parabola. The horizontal component of velocity velocity u cos remains unchanged h u where as vertical vert ical component decreases de creases up to t o the maximum maximum height height and then t hen increases . S : u sin  s (a) Time Time taken to reach the height height point tH = h g t a M u 2 sin 2  , (b) (b) Maximum height H = s 2g e s s 2 u sin  a (c) Total time t ime of flight flight = = 2 tH l g C o k u 2 sin 2  2 e (d) (d) Horizontal range = (ucos (u cos ) . T = (u cos ) (u sin sin ) = T g g

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(f) VELOCITY & DIRECTION OF MOTION AT A GIVEN TIME : Vcos ucos  Squaring & adding these 2 equations equat ions we will will get the velocity of the

projectile. le. Divi Dividi ding ng the veloci velocities ties in y and x direction directionss gives gives the directi direction on of usingt  projecti

Vsin

motion.

(g) VELOCITY & DIRECTION OF MOTION AT A GIVEN HEIGHT h :

u 2 cos 2    on adding V2 = u2  2 gh 2 2 2 2 V sin  u sin  2gh 

3

V 2 cos 2 

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(h) EQUATIONS OF MOTION IN VECTOR NOTATION :

. 1 8  1   8 S 1 2 8 u gt ( Vav = average velocity vector) (i) V u gt (ii) S ut gt (iii) Vav = 5 t 2 2 0 3 9 (i) EQUATION OF TRAJECTORY : 8 9 gx 2 0 x 1 Oblique Oblique Projection (refer fig-1) y = xtan x tan = x tan , R 2u 2 cos2 9 7 7 dy 7 Note that represent the direction of motion . 3 dx 0 9 PROJE PROJECT CTILE ILE UP AN INCLI INCLINE NED D PLANE PLANE : 3 0 9 (a) Total tim t imee of o f flight flight on o n the t he inclined inclined plane 0 : 2 u sin (   ) e T= n o g cos  h P (b) (b) Range PQ on the inclined inclined plane plane l a p 2 2     c o s . s i n ( ) 2u o u h PQ = = [sin (2 ) sin ] 2 B cos  g g cos 2  , ) r i  S . (c) For Maxmim Maxmimum um range 2 = = K 2 4 2 . Hence the direction for maximum maximum range bisects the angle between the vertical and the incli inclined ned R . S plane plane . ( a y u2 i r (d) (d) R max = a g (1  sin ) K . R (e) Greatest distance of the projectil pro jectilee from the t he inclined inclined plane plane ; g a 2 2 h u sin (  ) u S= when the projectil pro jectilee is at H, its velocity perpendicular to the plane p lane is zero . S 2 g cos  : s PROJE PROJECT CTILE ILE DOWN DOWN AN INCLINE INCLINED D PLANE PLANE : h t a 2 u sin (  ) M (a) Time of flight flight = , s g cos  e s 2 s 2 u sin (   ) . c os  a l (b) (b) Range OP = 2 C g cos  o k 2 e u T (c) Maximum range = 

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Get Solution of These Packages & Learn by Video Tutorials Tutorials on www.MathsBySuh www.MathsBySuhag.com ag.com EXERCISE – I

mQ.1 o c . g a h uQ.2 S y BQ.3 s h t a M . wQ.4 w w & mQ.5 oQ. 5 c . s e s s a l Q. 6 CQ.6 o k e T . w w w : e t i s b e wQ.7 m o r f e gQ.8 a k c a PQ.9 y d u t SQ.10 Q. 10 d a o l nQ.11 w o

A butte butterf rflly is fly flying with with vel velocity ocity 10 ˆi  12 jˆ m/s and wind is blowing along x axis with velocity u. If butterfly starts motion mot ion from from A and after some time reaches point point B, B, fin find d the value value of u. Find Find the chang changee in vel veloci ocity ty of the tip tip of the the minute minute hand hand (radius (radius = 10 cm) cm) of a clock clock in 45 minute minutes. s.

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A, B & C are three three objects objects each each movin moving g with constant constant veloci velocity ty.. A's A's speed speed is is 10 m/sec m/sec in a direction direction PQ . . The velocity of B relati relative ve to A is 6 m/sec at an angle of, cos 1 (15/24) to t o PQ . The velocity of C relative 1

8 8 8 5 -1 Rain Rain is is fal fallling vert vertiica callly wi with a speed speed of of 20 20 ms ms relative to t o air. A person perso n is running in the rain with a 0 3 velocity of 5 ms –1 and a wind is also blowing with a speed of 15 ms –1 (both towards to wards east). east) . Find the angle angle 9 8 9 with the vertical at which the person pe rson should hold his umbrella umbrella so that he may not not get drenched. d renched. 0 , 9 The vel velocity ocity-tim -timee graph graph of the partic particle le movin moving g along along a straight straight lin linee is is shown. shown. The The 7 7 –2 7 rate of o f acceleration and decel deceleration eration is constant and it is equal to 5 ms . If the 3 average averag e velocity during the motion is 20 ms –1, then find the value of t. 0 9 3 0 9 The fig fig.. shows the v–t v–t graph of a partic particle le movi moving ng in in straight straight lin line. e. Find Find the time time when when partic particle le returns returns 0 : e to the t he starting point. point. n o h P l a p o h B , ) r i S . K . R . S A particl particlee is proj projected ected in in the X-Y plan plane. e. 2 sec after after projecti projection on the vel veloci ocity ty of the parti particl clee makes makes an ( a angle 45° with the X - axis. axis. 4 sec after pro jection, it moves horizontally horizontally. Find the velocity of i y r pro jection jectio n (use g = 10 ms –2 ). a K . R A stone stone is dropped dropped from from a hei height h . Sim Simultaneo ultaneousl usly y another another stone stone is is thrown up from from the the ground ground g a with such a velocity that it can reach a height height of 4h. Find Find the t he time when two stones st ones cross each other. other. h u S : s A particl particlee is is projected projected upwards upwards with with a veloci velocity ty of 100 100 m/sec m/sec at an angl anglee of 60° with with the vertic vertical al.. Fin Find d the h t a time when the particle will move perpendicular perp endicular to its initial di direct rection, ion, taking g =10 m/sec2. M , s e A balloon balloon is is ascen ascendin ding g vertical vertically ly with with an accel accelerati eration on of 0.2m/s 0.2m/s2. Two stones are dropped from it at an interval interval s s of 2 sec. Find Find the distance d istance between between them 1.5 sec after the second seco nd stone is released.(use g=9.8m/s2) a l C o A large number of bullets bullets are fired fired in all direction with with the same speed v. What is the maxim maximum um area on k e ground on which these bullets bullets can spread? T

to B is 12 m/sec in a direction QP , then t hen find find the magnitude of the t he velocity of C.





Get Solution of These Packages & Learn by Video Tutorials Tutorials on www.MathsBySuh www.MathsBySuhag.com ag.com Q.12

m o c . gQ.13 a h u S y BQ.14 s h t a M . Q.15 w w w & m oQ.16 Q. 16 c . s e s s a l C oQ.17 k e T . w w wQ.18 : e t i s b e w m o r f Q.19 e g a k c aQ.20 PQ. 20 y d u t SQ.21 d a o l n w oQ.22

A boat starts from from rest from from one end end of a bank bank of a river river of width width d flowin flowing g with with velocity velocity u. The boat boat is steered with constant co nstant acceleration a in a direction perpendicular to the t he bank. bank. If point of start is origin, direction of bank is x axis and perpendicular perpendicular to bank is y axis. axis. Find the equation of o f trajectory trajecto ry of the boat . A ball ball is is thrown horizontal horizontally ly from a cliff cliff such that that it strikes strikes ground after after 5 sec. The line of sight from the point of projection project ion to the point po int of hitt hitting ing makes makes an angle of 37° with the ho horizontal. rizontal. What is the initial initial velocity velocity of projection. pr ojection. A ball ball is is projected projected on smooth incl inclin ined ed plane plane in in direction direction perpen perpendic dicula ular r to line line of greatest slope with velocity of 8m/s. Find Find it’s speed after after 1 sec.

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. 1 8 8 8 5 A partic particlle is proj projecte ected d from from poin pointt P with vel veloci ocity ty 5 2 m/s perpendicular 0 3 to the surface of a hollow right angle cone whose axis is vertical. vertical. It collides collides 9 8 at Q normally no rmally.. Find the time t ime of the t he flight flight of o f the particle. part icle. 9 0 , 9 7 7 Find Find range of projectil projectilee on the incl inclin ined ed plane plane which which is projected projected perpendicula perpendicular r 7 to the incline incline plane with velocity 20m/s as shown in figure. figure. 3 0 9 3 0 9 0 : Initial Initial acce accele leration ration of a particl particlee moving moving in in a straight straight lin linee is a0 and initial velocity is zero. The acceleration e n o h a0 reduces continuously co ntinuously to half in in every t0 seconds as a = . Find the terminal ter minal velocity of the particle. par ticle. P t l a t0 p 2 o h B Find Find the accel accelerati eration on of movab movable le pull pulley ey P and and block block B if , ) 2 . r i S . K . R . S ( a y i r a The veloc velociti ities es of A and B are marked marked in in the the figure. figure. Fin Find d the vel velocity ocity of K . block block C (assume (assume that that the the pulley pulleyss are are ideal ideal and string string inex inextensi tensibl ble). e). R g a h u S A particle is moving moving in x-y x-y plane such that x = t + sin(t) meter meter , y = cos (t) meter. meter. t is the time time in sec. Find Find : s the length of the path taken by the particle particle from t = 0 to t = 2 sec. h t a M , s The speed speed of a particl particlee when when itit is at at its greate greatest st heig height ht 2 5 is of its speed when it is at its half the e s s maximum height. The angle of o f projection projectio n is is ______ _____ _ and the velocity vector vect or angle ang le at half the maximum maximum l a C height is ______ . o k e T a

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Get Solution of These Packages & Learn by Video Tutorials Tutorials on www.MathsBySuh www.MathsBySuhag.com ag.com Q.23 Q.2 3 The horizontal horizontal range of a projectil projectiles es is is R and the maxim maximum um height height attained attained by itit is H. A strong wind wind now begins to blow in the direction of motion of the pro jectile, jectile, giving giving it a constant horizontal m acceleration = g/2. Under U nder the same conditions conditions of projection, pro jection, find find the horizontal ho rizontal range of the projectile. projectile. o

c . gQ.24 A rocket is is launc launched hed at an angl anglee 53º to the horizontal horizontal with an ini initial tial speed of 100 ms ms1 . It moves along a its initial line of motion mot ion with an acceleration accelerat ion of 30 ms2 for 3 seconds. At this time its engine falls & the h u rocket ro cket proceed pr oceedss like like a free body. Find Find : e S g y(i) the the maxi aximum alti altitu tude de reac reache hed d by the the rock rocket et a p B(ii) tot total time of flight . s h . the the hori horizo zont ntal al rang rangee . [ sin sin 53º 53º = 4/5 4/5 ] t (iii) 1 a 8 8 M 8 particle is is thrown horizontal horizontally ly with relative relative veloci velocity ty 10 m/s from an incli inclined ned . Q.25 A particle 5 w 0 plane, plane, which which is also also moving moving with accel accelerati eration on 10 m/s2 vertically upward. upwar d. Find 3 w 9 2) the time t ime after a fter which it lands on the plane (g = 10 m/s 8 w 9 0 & List of recommended questions questi ons from I.E. Irodov. , m 9 7 1.1, 1.4 to 1.8, 1.10, 1.11, 1.14, 1.15, 1.17, 1.18, 1.19, 1.21, o 7 c 7 1.24, 1.26, 1.27, 1.31, 1.32, 1.33, 1.34(a) . 3 s 0 e 9 s 3 s 0 9 a l 0 : C o e n k o e h T P . l w a p w o h w B , : ) r i e t S i . s K . b R e . w S ( a m y i r o r a f K . e R g g a a k h c u S a : P s h y t a d M u t , s S e s d s a a l C o l o n k e w T o 6







Get Solution of These Packages & Learn by Video Tutorials Tutorials on www.MathsBySuh www.MathsBySuhag.com ag.com EXERCI EXER CISE–I SE–II I

mQ.1 o c . g a h u SQ.2 yQ. 2 B s h t a Q. 3 M . Q.3 w w w &Q.4 m o c . s e s s a l CQ.5 o k e T . w w Q. 6 wQ.6 (a) : (a) e t i (b) s bQ.7 e w m o r f e gQ.8 a k c

A train train takes takes 2 min minutes utes to acqui acquire re its its full full speed 60kmph 60kmph from from rest rest and 1 minute minute to come come to rest from from the full speed. If I f somewhere in between two stations 1 km k m of the track be under repair and the t he limited limited speed speed on this part be fixed fixed to 20kmph, find find the late running running of the train t rain on account of o f this repair work, assuming assuming otherwise other wise normal at running of the train between the stations. st ations. 7

A speeder speeder in in an automobile automobile passes passes a stationary policeman policeman who is is hiding hiding behind behind a bil billl board with with a motorcycle. After a 2.0 2. 0 sec delay (reaction (react ion time) the policeman accelerates accelerates to his maximum maximum speed of o f 150 km/hr in 12 sec and catches the speeder 1.5 km beyond the billboard. Find the speed of o f speeder speed er in km/hr. km/hr.

e g a p

. 1 8 8 A particl particlee is is movi moving ng on a straight straight line. line. Its displ displacem acement ent from from the the ini initial tialposition position 8 5 is plotted plott ed against time in the graph shown. What W hat will be the velocity velocity of the 0 3 particle particle at 2/3 sec? sec? Assume Assume the graph to be a sine sine curve. curve. 9 8 9 0 A glass glass wind wind scree screen n whose whose incl inclin inati ation on with with the vertical vertical can be chan changed, ged, , 9 is mounted on a cart as shown in figure. The cart moves uniformly uniformly along along 7 7 the horizontal ho rizontal path with w ith a speed of 6 m/s. At At what maximum angle to 7 3 the vertical can the wind screen be placed so that the t he rain drops falling falling 0 9 vertically vertically downwards with velocity velocity 2 m/s, do not enter the cart? cart ? 3 0 9 An aeroplane aeroplane is is observed observed by two persons travelli travelling ng at at 60 km/hr km/hr in in two vehi vehicle cless movin moving g in in opposite opposite 0 : directions on a straight road. ro ad. To an observer in one vehicle vehicle the plane appears to cross cr oss the road ro ad track at e n o right angles while while to the t he observer in the other ot her vehicle vehicle the angle appears to t o be 45°. At what angle does does the t he h P plane plane actually actually cross the road track and what is its speed relative relative to the ground. l a p o How long long will will a plan planee take to fly fly around around a square square with with side side a with with the wind wind blowi blowing ng at a veloci velocity ty u,inthe two cases cases h B , the direc directi tion on of of the the wind wind coin coinci cides des with with one one of the sides sides ) r i the directi direction on of the wind wind coinci coincides des with with one diagona diagonall of the square. square. The vel velocity ocityof the plane plane in in stil stilll air air is v > u. S . K . Two shi ships ps A and B original originally ly at a distanc distancee d from from each each other depart depart at the same same time time from a straigh straightt R . coastline. Ship A moves moves along a straight st raight line line perpendicular perpendicular to the shore while ship B constantly heads heads for ( S a ship A, having at each eac h moment the same speed sp eed as the t he latter. After a suffici sufficiently ently great interval of time time the y i r second ship will obviously obviously follow follow the first one at a certain cert ain distance. Find Find the t he distance. a K . The The slope slopess of the win wind-scre d-screen en of two motor motorca cars rs are are 1= 300 and 2 = 15 150 respectively respec tively.. The first car ca r is R g a travell trave lling ing with a velocity of v1 horizontally hor izontally.. The second sec ond car ca r is travell tr avelling ing with a velocity v2 in the same h u

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m o c . g a h u SQ.11 y B s h t aQ.12 M . w w w & (a) m(a) o(b) c . s(c) e(d) (d) s s(e) a l C oQ.13 k e T . w wQ.14 w : e t i s b eQ.15 w m o r f e g a k c

A hunter is ridin riding g an elephant elephant of height height 4m moving moving in in straight straight line line with uniform uniform speed of 2m/sec. 2m/sec. Adeer running running with a speed V in front front at a distance of 45m moving moving perpendicular to the direction of motion of o f the elephant. If hunter can throw t hrow his spear with a speed of 10m/sec. relative r elative to the elephant, tthen hen at what angle  to it’s it’s direction of o f motion must he throw t hrow his spear horizontally horizont ally for a successful succe ssful hit. hit. Find also th t he speed ‘V’ ‘ V’ of the deer. dee r. A projectil projectilee is to be thrown horizontal horizontally ly from the top of a wall of height height 1.7 m. Calcul Calculate ate the init initial ial velocity of projection projectio n if it hits perpendicularly perp endicularly an incline incline of angle 37º which starts star ts from fro m the ground at the t he bottom of the wal wall. l. The line line of greatest greatest slope slope of incl inclin inee lies lies in the plane plane of motion motion of projectil projectile. e.

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. 1 8 Two incl inclin ined ed planes planes OA and OB havi having ng incl inclin ination ation (with horizontal) horizontal) 30° 8 8 and 60° respectively re spectively,, intersect each other ot her at O as a s shown in fig. A particle part icle is is 5 0 –1 projected from point P with with velocity velocity u = 10 3 m s along a direction 3 9 8 perpendi perpendicul cular ar to plane plane OA. If the particl particlee strikes strikes plane plane OB perpendi perpendicul cularl arly y 9 at at Q, calculate 0 , velo veloci city ty with with whi which parti particl clee stri strikes kes the plan planee OB, OB, 9 7 time of flight, 7 7 verti erticcal height h of P from rom O, 3 0 maxi aximum hei height ght from from O attai attaine ned d by the parti particl clee and and 9 3 distance PQ 0 9 0 : A parti particl clee is is proje projected cted with with a vel veloci ocity ty 2 ag so that it just clears two wall wallss of equal height 'a' whi which ch are e n o h at a distance '2a' apart. apart . Show Sho w that the t he time of passing passing between the walls is is 2 a g . P l a A stone is is projected projected from the point point of a ground in in such such a direction direction so as to hit hit a bird bird on the top of a p o h telegraph post of height h and then attain the maximum maximum height 2h above the ground. If at the t he instan instantt of B , ) projection, the bird were to fly away horizontally horizontally with with a uniform speed, find the ratio between the i r S horizontal horizont al velocities of the bird and the stone, sto ne, if the stone still st ill hits the bird while descending. . K . R Two Two persons persons Ram and Shya Shyam m are are throwin throwing g ball ball at each other as shown shown . S ( in the figure. The maximum horizontal horizonta l distance from fro m the building where a y Ram can stand and still throw a ball at Shyam is d 1. The maximum i r a horizontal distance of Ram from the building building where Shyam can throw a K . R ball ball is d 2. If both bot h of them can throw ball with a velocity of 2gk , find g a the ratio of d 1/d 2. Neglect the height of each person. h u






EXERCISE # III m oQ.1 c . g a h u S y B s h t aQ.2 M . w w w (a) & (b) m o c . sQ.3 e s s a l C oQ.4 k e T . w w w (a) (a) : e t i s b(b) e w m o r Q.5 f e g a k(i) c

The motion otion of a body body is gi given ven by by the equati equation on

d v (t ) = dt

6.0

 3 v(t) ; where v (t) is the speed in

m/s & t in sec., if the body has v = 0 at t = 0 then (A) the termina t erminall speed is 2.0 m/s (B) the t he magnitude of the initial acceleration accelerat ion is 6.0 m/s² (C) the speed varies with time time as v(t) = 2 (1  e-3t) m/s (D) the speed is 1.0 m/s when the acceleration is half the the initial value.

9

[JEE ’1995]

e g a p

. 1 Two guns, guns, situated situated at the top of a hil hilll of hei height ght 10 m, m, fire fire one shot shot each each with with the the same same speed speed 8 8 8 5 3 m/s at some interval of time. time. One gun gu n fires fires horizontally horizont ally and other ot her fires upwards at an a n angle of 60° 5 0 3 with the horizontal. hor izontal. The shots sho ts collide in air at a point po int P. P. Find 9 8 the time interval interval between the firi firings, ngs, and 9 the coordinates coo rdinates of the point P. P. Take Take origin of the coordinates system at the foot of o f the hill hill right below the 0 , muzzle and trajectories in X-Y plane. [JEE'1996] 9 7 7 7 The trajector trajectory y of a project projectil ilee in in a verti vertical cal plan planee is is y = ax ax bx2, where a, b are constants & x and y are 3 0 respectively the horizontal & vertical distances of the projectile p rojectile from the point of o f projection . Th T he maximum maximum 9 3 hei height ght attai attained ned is is ____ ______ __ & the the angl anglee of proj projec ecti tion on from from the hori horizontal zontal is ______ ______.. [JEE [JEE '1997] '1997] 0 9 0 : A larg largee heav heavy y box box is is slid slidin ing g withou withoutt fricti friction on down a smooth smooth plan planee of e n o inclination . From a point P on the bottom bott om of a box, a particle iiss projected h P inside inside the box. The initial initial speed of the particle par ticle with respect to t o box is u l a and the direction of pro projection jection makes an angle angle with the bottom as p o shown show n in figure. figure. h Find Find the the distan distance ce along along the the bottom bottom of the box box betwee between n the the point point of projecti projection on P and and the the point point Q wher wheree B , ) r i the particle lands. (Assume that the particle does not hit any other surface of the box. Neglect air S . resistance). K . If the the horizon horizontal tal displ displacem acement ent of the particle particle as seen seen by an observ observer er on the the ground ground is is zero, zero, find find the the speed speed R . of the the box box with with respe respect ct to the the ground ground at the the ins instant tant when when the parti particl clee was was proje projected. cted. [JEE'1 [JEE'1998] 998] S ( a y r A partic ticle of mass 102 kg is moving slong the positive x-axis under the influence of a force i a K K . F(x) = where K = 102 N m2 . At time t = 0 it is at x = 1.0 m & its velocity is is v = 0 . Find Find : R 2 2x g a its veloci ocity when it re reac ach hes x = 0.5 0.50 0m h u

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Get Solution of These Packages & Learn by Video Tutorials Tutorials on www.MathsBySuh www.MathsBySuhag.com ag.com Q.8

m o c . g a h u S y B s h t Q.9 a M . w w w & m o c . sQ.10 eQ. 10 s s a l C o k e (a) T . (a) w w w(b) (b) : e t i Q.11 s b e w m o r f Q.12 e g a k c

A bal balll is dropp dropped ed verti vertica callly from a hei heigh ghtt d above above the ground gro und it hits the ground and bounces bou nces up vertically vertically to a height d /2. /2. Neglecti Ne glecting ng subsequent motion aand nd air resistances, its velocity v varies with the height h above the ground as [JEE'2000 (Scr)]

(A)

(B)

(C)

0 1

(D)

e g a p

. 1 8 8 8 5 0 3 9 8 9 0 , 9 7 7 7 3 On a fricti frictionl onless ess horizon horizontal tal surface, surface, assum assumed ed to be the x-y plane, plane, a smal smalll trolley trolley 0 9 A is moving moving along a straight line parallel to the t he y-axis (see figure) figure) with a constant const ant 3 0 9 velocity of ( 3  1) m/s. At a part icular instant instant,, when the line line OA makes an 0 : angle of 45° with the x-axis, x-a xis, a ball is thrown throw n along the surface sur face from the origin or igin e n O. Its It s velocity makes makes an angle with the x-axis x-a xis and it hits the trolley tr olley.. o The motio motion n of the bal balll is is observ observed ed from from the fram framee of trolle trolley y. Calcul Calculate ate the the angle angle made by the velocity h P l vector vecto r of the t he ball with with the th e x-axis in in this frame. a p 4 o Find Find the the spe speed ed of the the bal ball with with res respec pectt to the the sur surffac ace, e, if if = . [JEE 2002] h B 3 , ) r i S A parti particl clee starts starts from from rest. rest. Its acc accel elera eration tion a) versus time (t) is as shown . K in the figure. The maximum maximum speed of o f the particl part iclee will be . R [JEE' 2004 (Scr)] . S ( (A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/s a y i r a A small small block block slides slides without friction friction down an an incli inclined ned plane plane starting from from rest. Let Sn be the dista distance nce K . Sn R g travell tr avelled ed from time t = n - 1 to t = n. Then S is is [JEE' 2004 (Scr)] a n 1 h

An objec objectt A is is kept kept fi fixed xed at the the poi point x = 3 m and and y = 1.25 1.25 m on on a plank P raised r aised above the t he ground. gro und. At time t = 0 the plank starts st arts 2 moving along the + x direction with an acceleration 1.5 m/s . At the same instant a stone ston e is projected from fr om the origin with a velocity u as shown. A stationary stat ionary person on the t he ground observes the stone sto ne hitting hitting the object during its downward motion at an angle of 45° to the horizontal. All the motions are in x-y plane. Find u and the time t ime after which the stone hits the object. o bject. Take Take g = 10 m/s2. [JEE 2000]

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ANSWER ANSWER KEY m o c . gQ. 1 a h u S yQ. 5 B s h t a Q. 9 M . w wQ. 13 w &Q.17 m oQ. 20 c . sQ. 23 e s s aQ.25 l C o k e T . Q. 1 w wQ. 4 w : e t i Q. 6 s b e wQ. 9 m Q.11 o r f e gQ.14 a k c

EXERCISE # I 6 m/s

     2  cm/min    3 

Q. 2

Q. 3

5 m/sec

Q. 4

tan –1(1/2) 1 1

5s

Q. 6

3 6 . 2 se c .

Q.7

20 5

v 4

Q. 10

50m

Q.11

100/3 m/s

Q. 14

10 m/s

Q. 15

a 0t 0 ln ( 2)

Q. 18

aP = 1 m/s2 , aB = 2 m/s2 

8m

Q. 21

600, tan-1

R + 2H

Q. 24

(i) 15 1503.2 m (ii) 35.54 sec (iii) 39 3970.56 m

1 3

32

G JK H

Q. 8

20 sec



h 8g

Q. 12

g2

1 sec

y=

a x2 2 u2

Q . 16 75 m



Q. 19

5 m/s

Q. 22

2asin(/2)

sec

EXERCISE # II ,

160 sec

Q. 2

122.7 km/hr

2 t an –1(1/3)

Q. 5

 = tan –12, v = 134.16 km/h

(a)

2a   v  v 2  u 2 



2

2

 , (b)

2 2 a   2v

2 2 1

Q. 12 Q.15

2



v u (a) 5d/4 tan, (b) 9, (c) point O u = 3m/s

Q. 3

v

2

u

 u 2  

2

Q. 10

S0 4

Q.7

d 2

Q. 8

3

 = 370, v = 6m/s

(a) 10 ms –1, (b) 2 sec, (c) 5 m, (d) 16.25 16. 25 m, (e) 20 m

k  h k  h

EXERCISE # III

e g a p

. 1 8 8 8 5 0 3 9 8 9 0 , 9 7 7 7 3 0 9 3 0 9 0 : e n o h P l a p o h B , ) r i S . K . R . S ( a y i r a K . R g a h

Kinematics Type 1

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