Kinematics Questions and Answers

A gravity assist or slingshot effect around a planet changes a spacecraft s velocity relative to the Sun by entering and leaving the gravitational field of a planet To accelerate the spacecraft flies with the movement of tr planet taking a small amount of the planet s orbital energy to decelerate the spacecraft flies against the movement of the planet The sum of the kinetic energies of both bodies spacecraft and planet remains constant ju like an elastic collision but without physical contact This can be assumed to be like a tennis ball bouncing off a moving train Imagine throwing a ball at 30 Kmph toward a train approaching at 50 Kmph The engineer of the train sees the ball approaching at 80 Kmph and thes departing at 80 Kmph after the ball bouncing elastically off the front of the train Because of the train s motion however that departure is at 130 Kmph relative to the station This explanation might seem to violate the conservation of energy and momentum but the spacecraff s effects on the planet have not been considered The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet though the planet s enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small These effects on the planet are so slight because planets are so much more massive than spacecraft that they can be ignored in the calculation The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the night places to enable a voyage to a particular destination For example the Voyager missions which started in the late 1970s were made possible by the Grand Tour alignment of Jupiter Saturn Uranus and Neptune A similar alignment will not occur again until the middle of the 22nd century Diagram shows a simplified version of satellite approaching earth The velocity of satellite after it suffers slingshot effect from earth relative to earth is u and relative to sun is v Find the value of v u Satellite 10 000 km h Earth 100 000 kam h 1 Gere

2 1 A 400 N block is dragged along a horizontal surface by an applied force F as shown The coefficient of kinetic friction is 0 4 and the block moves at constant velocity The magnitude of F is 3 F 3 5 F A 100 N B 150 N 4 5 F C 200 N D 290 N

A uniform but heavy rope of length L is suspended from a ceiling A small transverse disturbance is produced at bottom The ratio of time taken to travel upper half to time taken to travel lower half of the string is 02 1 0 2 1 1 Data is not sufficient to determine the ratio

A body is thrown vertically up with some velocity at t 0 crosses a fixed point Pin its path at t 4 s and again at t 6 s The velocity of projection of the body will be O 20 m s O 50 m s O 10 m s 40 m s

A boat is moving with velocity 41 61 m s with respect to ground The water in the river is moving with 31 4 m s with respect to ground The velocity of boat with respect to water is O 7i 10 m s O 1 2 m s O 51 7 m s O 51 8 m s

A body projected horizontally from the top of a tower with initial velocity 30 m s hits the ground at an angle 60 with the horizontal The vertical component of velocity at the time of hitting the ground is O 10 3 m s O 30 3 m s O 30 m s 15 m s

Paragraph Two cars A and B are initially at rest on the same road on adjacent lanes 300 m apart Att 0 they start moving towards each other with constant acceleration a and a 2 respectively Immediately after they cross each other the cars A and B decelerate at constant rate 5a 2 an arespectively until they come to rest The total time for which the car A moves is 14 seconds The total distance in metres that car A covers is

9 A ball of mass 100 g at rest is thrown on a horizontal surface as shown in the figure The acceleration displacement graph for the motion is given The maximum height attained by the ball on the smooth inclined plane is a m s X 0 1 10 m x 10 m 5 4 3 2 1 24 6 8 10 2 4 m 3 x m

m 4 A girl throws a ball horizontally with velocity u from a height directly towards a vertical wall at a distance L After colliding with the ground once the ball hits the wall horizontally at a point P as shown The height of the point P above the ground is given by h hoose the answer 2 L gh M L

The variation of radius of a circle with time is given by the relation r 2t 3 m where t is time in second The rate of change of area of the circle at t 1 s will be O 20 m s O 10 m s O 15 m s O Zero

A cone of height H and base radius r is hanging vertically with the help of string inside the liquid of density Po as shown The net force acting on th curved surface of the cone by the liquid will be ignore atmospheric pressure 4 A PogH r C 2po gH R2 H Po B PogHtr 2 D Po D Po gH r

An object is released at one bank into a river flowing with speed 5 km h towards east Air is blowing with speed 5 km h towards north If width of river is 200 m then minimum time taken by floating object to reach the other bank is consider ideal situation 1 144 minute 3 144 second 2 3 4 second 4 14 4 second

In figure shown the graph shows the variation of a acceleration a acting on a body of mass 10 kg in gravity free space with time t The velocity of the body at t 0 is zero a m s The average acceleration of the body from t 0 tot 15 s is 2 1 10 15 25 30 t s

A particle is moving in a plane and the trajectory is given by r t aet and 8 t At At any time t the correct pair of amplitude of its velocity and acceleration are 4 Zalet and 2a e t O Option 4 2alent and 2a e t Option 1

A projectile is projected with velocity 30 m s at an angle of 60 with horizontal At time t to projectile velocity is perpendicular to its initial velocity Let speed of projectile at that instant be v then answer the following question g 10 m s Value in

26 If an object is thrown at an angle of 60 with horizontal end elevation angle of the object at its highest point as seen from the point of projection a tan b tan 2 c tan 1 2 1 2 d None of these

Two forces and F 81 4 N act on an object of mass 2 kg that is initially at rest at coordinates 2m 4m Find velocity of the object at t 10 s 451 151 151 451 451 151

A body covers one third of the distance with speed v the next one third of distance with 3v 2 speed and the remaining one third of the distance with speed 22 The average speed 2v 2v 3 3 is Only One Correct Answer A B C D 14v 15 18v 19 12v 19 Review 19v 18 6

On turning a comer a motorist rushing at 40 m s finds a child the road 108 m ahead He instantly stops the engine and a the brakes so as to stop it within 1 m of the child what time apple required to stop it a 5 4 second c 3 9 second b 6 4 second d 2 second

in rotating body 32 Derive an expression for escape speed of a body torque and angular momentum of a of a particle VI Answer any THREE of the following questions PART E 33 A car moving along a straight highway with a speed of 126 kmph is brought to rest within a distance of 200 m Calculate the retardation of the car assumed to be uniform and how long does it take for the car to come to rest 34 A football player kicks a ball at an angle of 30 to the horizontal with an initial velocity of 20 ms 1 Calculate i maximum height reached ii horizontal range of the football Given g 9 8 ms 21 35 Water is pumped from a mine 40 m deep at the rate of 600 litres per minute Calculate the power required 36 A particle is moving at a speed of 12ms 1 on a circle of radius 2m If the speed of the particle is increased to 15 ms 1 in two second What is the angular acceleration produced 37 Calculate the orbital velocity and period of revolution of an artificial satellite of earth moving at an altitude of 200 km Radius of the earth 6400 km mass of earth 6 x 1024 kg G 6 7 x 10 11 Nm kg 2 3 x 5 15

A conical frustum of height h has been placed with its axis vertical A particle of mass m is projected horizontally with velocity vo along its upper brim The radii of its upper and lower cross sections are R and r R 2 respectively The particle slides along the inner surface in spiral path without friction and leaves the lower face at point B a Find the horizontal and vertical B component of velocity of the particle as it leaves the frustum at B b Find minimum value of h for which the particle will neve out of the frustum Vertical axis A R 10 h

A woman bails out of an airplane at an altitude of 11 000 ft falls freely for 24 s then opens her parachute How long will it take her to reach the ground Assume linear air resistance v ft s taking p 0 15 without the parachute and p 1 5 with the parachute Suggestion First determine her height above the ground and velocity when the parachute opens It will take her seconds to reach the ground Round to the nearest whole number as needed

A man throws a ball vertically upward and it rises through am and returns to his hands what was the ascent initial velocity of the ball and for how much time T it remained in a T 5 sec u 20 3 m s T 5 64 sec u 10 2 m s T 5 64 sec u 20 2 m s

4 s the ary on er at to 3 25 Figure given below shows the graph of velocity v of particle moving along x axis as a function of time t Average acceleration during t 1 s to t 7 s is 30 20 0 1 1 5 m s 3 2 m s v m s 2 68 t s 2 1 m s 4 2 5 m s

A 10C charge is placed near a neutral body whose other end is earthed The dielectric constant of neutral body is 5 then find the maximum charge induced on neutral body a 8 c 8 b 12C d 2

91 m b 182 m c 293 m d 111 m A particle moves along X axis The velocity of the particle as function of x is V2 12x 3x SI Find velocity of particle at the instant when acceleration is 1 5ms a 3ms b 4ms c 1 5ms Displacement time graph is shown in the figure d zero

A block of mass 9 kg is lying on a rough horizontal surface A particle of mass 1 kg strikes the block with a speed of 50 m s at an angle of 37 with the vertical and sticks to it The frictional coefficient between the ground and the block is 0 4 Find the velocity of the combined system just after the collision assuming limiting friction coefficient between the block and the ground after the collision A Less than 1 4 m s C Greater than 1 4 m s B Equal to 1 4 m s D None of the above 1 ka 50 m s 9 kg 0 4

Speed of particle moving in a circle of radius 2 m varies with time t as v 2t m s where t is time in second For what value of time t acceleration makes an angle of 45 with velocity

A ball thrown in upward direction reaches to a maximum height of 100 m If the time taken to cover the first 50 m is t and that to cover the remaining 50 m is t2 then Only One Correct Answer A B C D t 1 t 1 t 1 Can t determine i

5 A projectile is fired from ground e above the horizontal Angle of elevat highest point from point of projection is 1 tan 2tan 0 2 tan o tan 0 1 3 tano tane 2 1 4 tano tan 2001 02001

10 An aeroplane is flying at constant height 1 96 km with speed 600 km h towards a point directly over a target At what angle of sight should it release a bomb if it is to strike the target on the ground 1 75 2 45 3 0 4 60

32 The diagram shows two projectiles thrown from the same point By looking at the diagram of their paths compare the time of motion YA A B X 1 TA TB 2 TB TA 3 TA TB 4 Initial velocity should be known to compare the

a A frictionless surface of 1 m length is inclined at an angle of 30 to the horizontal as shown in figure 58 Calculate i how long it would take the object to slide down and ii how fast the object would be going at the bottom s ut 1 at T sin Zd 14 mg sin 0 8 30 N s g S X m g mg cos 0 Sc

A boy of mass 40 kg is on a plank of mass 40 kg moving to right on a smooth floor at 8 m s H wants to jump on to an identical plank travelling in the front at the same speed With what minimum speed in m s relative to the plank on which he is standing should he jump Take g 10 m s 40 kg 8m s 5 m 40 kg h 8m s

3 A particle is projected horizontally with speed u from top of a tower The particle reaches the ground in time T The value of speed of the particle by which it will strike the ground is 1 u gT 3 u g 7 2 u g T 2 4 u 2g T

The initial velocity of a particle is 21 33 m s A constant force F A Its velocity is constant B Its path is parabolic Oc its path is straight line Op it moves on a circular path 41 31 N acts on the particle Hence

A car covers first half part of its journey with a velocity v and the remaining part of the distance was covered in time t The remaining distance was covered with velocity v for of time t and with velocity v for the next of time t Then 1 The average velocity of car of whole journey is aks 2 The average velocity of car of whole journey is 4 YJU S 2V3 3v V2 2V3 V V2 V3 3v V2 V3 3 The ratio of time taken by car in first half distance to time taken by car in next half distance is V2 2V3 3v1 2v Vz The ratio of time taken by car in first half distance to time taken by car in next half distance is

A ball is dropped downwards from top of tower After 1 second another ball is dropped downwards from the same point What is the distance between them after 3 seconds take 9 10m s O O O O 50 m 25 m 20 m 9 8 m

A frictionless rod ABC and a particle P of mass 1 kg are lying on a frictionless horizontal floor as shown in view of the situation The portion AB of the rod is bent to form quarter of a circle The rod is suddenly mad move with a constant velocity 10 m s towards right along portion BC What is the work done by the rod on particle till it leaves the rod B D 100 Joule 200 Joule 50 Joule 150 Joule B

A particle of unit mass is projected with velocity u at an inclination a above the horizon in a medium whose resistance is k times the velocity Its direction will again make an angle a with the horizon after a time 2ku g a log 1 c 1 sina Mb log 1 sina k log 1 kusin a 2ku g 2ku d log 1 sin a

2 4 2000 N 1 1000 N 3 1500 N 28 A and B are of mass m and C is of mass M If the system is in equilibrium then U C M A B m m 1 M 2m 2 M 2m 3 M 2m 4 M m 0 Aakash Educational Services Limited Road Ost can be pla slipping is s 0 5 E Where x ar 1 30 cm 3 40 cm

The maximum height of projectile is X y 2x 2 Symbols have usual meanings and Sl unit 1 4 m 2 1 m 3 2 m 4 10 m 35 A projectile is thrown up at angle e to the horizontal ground from a fixed point and it hits the ground following parabolic path The magnitude of tangential acceleration w r t fixed point 1 Increases continuously 2 Decreases continuously 3 First decreases then increases 4 First increases then decreases SECTION C 5 re with speed VA anc period of rotation is t speed of A to that of 1 TATB 3 TB TA The x and y coordi are x 5t 2 a 6 and y are in m acceleration of th 1 O 3 4 m s In the given f total acceler clockwise dire

If t is time en Motion in a Straight Line 65 A boy is standing on a plank which is accelerating vertically upwards with constant acceleration If boy throws a ball vertically up with velocity vo relative to plank and its time of flight is T the acceleration of the plank is 1 a 2v gT T K aT 2 a LAY Vo gT T 2vo gT

eed en e al 28 A projectile is projected at some angle from the ground towards east in the absence of air resistance then time period and range of projectile are T and R If wind starts blowing towards east with some acceleration then the new time period T and range R have the relations 1 T T and R R 2 T T and R R 3 T T and R R 4 T T and R R 29 A gun is fitted on platform moving with velocity

A cylindrical empty vessel is kept vertically with its open end up on a horizontal ground when it rains uniformly and vertically The rate of filling in the vessel with rain water will O remain unchanged if its length is made inclined to the vertical decrease if its length is made inclined with the vertical remain unchanged if a slow wind blows horizontally decrease if a slow wind blows horizontally

Ramlal plan in new year to go Rajgir with his group of friends to enjoy and party He start s to move with a car from madhepura to sa harsa with a speed of 40 km hr in 2 hrs Th en he move from saharsa to patna with a sp eed of x km hr in 5 hrs Find the average sp eed

A plane traveling horizontally at 30 0 m s at an altitude of 1 85x10 2 m drops a package to people below Where in meters does the package hit the ground horizonally relative to where it was dropped Note Your answer is assumed to be reduced to the highest power possible

48 A particle projected from ground moves at angle 45 with horizontal one second after projection and speed is minimum two seconds after the projection The angle of projection of particle is Neglect the effect of air resistance 1 tan 3 3 tan 2 2 tan 2 4 tan 4

15 The velocity v varies with displacement x as shown in the graph The acceleration v m s V U v d 0 O 1 Is constant 2 Increases with time 3 Decreases with time x m

As shown in the figure M is a man of mass 60 kg standing on a block of mass 40 kg kept on ground The co efficient of friction between the feet of the man and the block is 0 3 and that between B and the ground is 0 1 If the person pulls the string with 100 N force then A B may slide on ground B A and B may move together with acceleration 1 m s C the friction force acting between A B may be 40 N D the friction force acting between A B may be 180 N A M B