Kinematics Questions and Answers

Two cars A and B moving with uniform velocity of 60 km h and 80 km h respectively in opposite directions If car A moves from point X and car B moves from point Y on a straight road which are 420 km apart and they meet at a point P between X and Y Find the ratio of the distances XP and PY A 7 5 C 6 7 B 3 4 D 7 6

A football player is lining up to take a penalty kick To score the penalty they need to kick the ball below a crossbar that stands 2 m away and at a height of 3 m above the ground and have a velocity of 24 8 m s to beat the goalkeeper The player strikes the ball and the ball has an initial velocity of 24 8 m s at an angle of 25 a Find the maximum height of the ball Give your answer to 3 significant figures 1 mark b Find the horizontal distance at this height Give your answer to 3 significant figures 1 mark m c Find the height at a distance 2m away Give your answer to 2 decimal places 1 mark d Does the player score the penalty 1 mark m m

A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate to come to rest If the total time elapsed is t seconds the tota JEE Main March 2021 distnace travelled is 2a a c 4a a B t a 26a B 2 b d t a B a 4 a B t

44 Four similar particles of mass m are orbiting in a circle of radius r in the same direction and same speed because of their mutual gravitational attractive force as shown in the figure Speed of a particle is given by c Gm 4r Gm E 1 2 2 1 2 2 m m r b m V Gm V r Gm d 1 2 2 2

A Train travelling at 20 km per hour is appro aching a platform a bird is sitting on a pole on the platform when the train is at a distan ce of 2 km from pole brakes are applied whi ch produces a uniform deceleration in it at that instant the bird flies toward the train at 60 km per hour and after touching the neare st point on the train flies back to the pole an d then flies toward the train and continues r epeating itself calculate how much distanc e the bird cover before the train stops

30 A 2 kg block is gently pushed from rest at A and it slides down along the fixed smooth circular surface as shown in figure If the attached spring has a force constant k 20 N m What is unstretched length of spring in m so that it does not allow the block to leave the surface until angle with the vertical is 0 60 2 R 1 5m B

The momentum P verses velocity V graph of two particles A and B having constant mass is given below Choose the correct statement about the mass of the particles P A tov V 1 A has more mass than B 2 B has more mass than A Both A and B have same mass A and R cannot be compared

11 A car on the cross road is moving towards east at a speed of 40 km hr Another car which is 1 km south of the crossing is approaching the crossing with the same speed Their closest distance of approach will be V 1 1 km boley dre 2 dt 2 2 km 1019 bas 5 km

53 A body thrown vertically up with initial velocity 52 m s from the ground passes twice a point at h height above at an interval of 10 s The height h is g 10 m s S 1 22 m 3 11 2 m 2 10 2 m 4 15 m 8

at the moment t 0 The ball bounces once on the smooth floor and then lands into cup C The coefficient of restitution for the collision is 0 8 Select the correct alternative g 10 m s A 2 6 1 5 m S 14 d 1 The time taken by the ball to reach B is 3 The ratio 2 m s 3 V10 2 The time taken by the ball to reach C is 3 10 S OC OB 2 6 B 4 The distance d is 52 3 10 10 7 r C Cup m

9 The velocity time graph in case of a stone thrown vertically upwards and returning back to the earth is shown by A velocity n Time I B velocity m s time s Page 2 of

88 There is a magnetic field acting in a plane downward perpendicular to sheet of paper Fig Particles in vacuum move in the plane of paper from left to right The path indicated by an arrow could be travelled by a proton c electron W X X X x X X X X X X X X X X X X X X X X X X X X X b neutron d a particle

30 A 2 kg block is placed on the rough horizontal surface of a truck at a distance of 6m from its rear end as shown in figure The coefficient of friction between the block and surface of track is us 0 20 and k 0 15 The truck starts from rest at t 0 and moves with constant acceleration a s 4 5 m sec Find the time t when 2 kg block will fall off the truck and the velocity of block at this instant Find the distan travelled by the truck upto that instant and also find the total horizontal displacement of block from the initial position until it strikes the road H 6m2 kg F 1 25 m

The position vector of a particle is given by r 2t 5t j m t is time in sec Then the angle no between initial velocity and initial acceleration is 4 then find the value of n

Answer each 11 An ultralight airplane has a bearing of N20 with an airspeed of 25 mph If the plane encounters a 10 mph wind blowing at a bearing of 545 what is the new speed and bearing of the ultralight

I want correct only otherwise I will give downvotes Q28 A bomber flies along a horizontal line at an altitude of 1500 m with a velocity of 400 km per hour 1 bomb should be dropped so as to hit the target on the ground Find at what horizontal distance before passing over a target on the ground a ii Calculate the magnitude and direction of the velocity with which the bomb will hit the target iii Where will be the bomber when the bomb strikes the target Take g 9 81 m sec

A gas is enclosed in a cylinder with a movable frictionle piston Its initial thermodynamic state state at pressure P 10 Pa and volume V 103 m changes to a fire 15 state at P 1 32 105 Pa and V 8 10 m in X adiabatic quasi static process such that p v5 constant Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps an isobaric expansion at P followed by an isochoric isovolumetric process at volume Vf The amount of heat supplied to the system in the two step process s approximately a 112 J JEE Advanced 2016 c 588 I b 294 J 010 I

2 33 A solid cylinder of length H diameter D and of relative density S floats in neutral equilibrium in water with its axis vertical What is the ratio of H to D if S 0 6 a 0 86 c 0 52 b 0 72 d 0 46

Comprehension 1 We know how by neglecting the and analysed Now we consider the case of of collision can be simplified by considering the case of elastic collision only When a a wall we can divide its velocity into two components one perpendicular to the wall a to the wall If the collision is elastic then the perpendicular component of reversed with the same magnitude Velocity just before collision A B Vcose Vsine their motion in air is correct A H H H Vcose Vsine Components of velocity Components of velocity just after collision just before collision B H H H ball is throw stant a pers projection Yes 60 particle is p K particle ha The other parallel component of velocity will remain constant if given wall is smooth I same angle with the horizontal The balls A B and C collide with the wall during their Now let us take a problem Three balls A and B C are projected from ground with all three collide perpendicularly with the wall as shown in figure velocity The maximum height attained by ball A from the ground is A 10 m B 15 m C 20 m 17 2 ur particle i 1 y x 3 xy ca water fe v the to A proje Which of the following relation about the maximum height H of the three balls from the 1 C H H H D H H R If the time taken by the ball A to fall back on ground is 4 seconds and that by ball B is 2 the time taken by the ball C to reach the inclined plane after projection will be A 6 sec B 4 sec C 3 sec D 5 sec v g boy ca hrow th 1 20 fg 1 ya D Insufficient

An aircraft is flying horizontally at a height of 1 km from the ground with a speed of 200 m s An anticraft missile launcher kept at a point on the ground which is in the vertical plane of the motion of aircraft Muzzle velocity of missile is 600 m s The missile is fired at a time when the aircraft was vertically above the anticraft missile launcher At what angle with horizontal should it be fired so as to hit the aircraft 1 sin 2 cos 2 6 G 3 3 tan 1 3

26 29 Wind is mane 30 a Wind V Jaa will be p 1 3j 28 9 is blowing 34 9 20m s The time blowing a 50cm with scunning after towards cast is velocity V towards nor towards north with acceleration neleich man will feel the 32 V a A vector p of magnitude dacting in x y plane 13 cu vectors p an angle with b 35 body is thrown vertically up with some finca ned Point Pin its path at 7 45 and at 68 the velocity of presjection of body will be b 50m s c lom s c 40m s velocity att 0 and agam crosses a 9 Jau Jau d ov a a rising vertically feed packet after Tom s Lit two bodies one held lacom directly released simultaneously from the large height both fall freely from above the other are and the separation que thee gravity the bodies just after b 100cm d 120cm d b 12m s A Person Sitting velocity throws a 9 80cm A Food Packets is released frem a 8 making helicopter which is at 2 m 3 the magnitude of velocity of as will be 9 lom s c 18 m s 9 5m s d Car moving at Constant in an open ball vertically up into aire The bels the hand water

A ball with radius r and mass m hangs in a string with length L and rests to a vertical wall See th figure above Decide the normal force N from the wall on the ball expressed by r m L and g Choose one alternative ON 2mg mg ON 2 2 Lr ON mg 2Lr ON mg ON 9 I 2Lr mg

L Lawliet threw a ball with a velocity 40m s at an angle of 45 with the horizontal towards a box which is 8m away and is located 6m above the ground The box has some special powers whenever an object collides with it with velocity v vector the object s velocity instantly changes to 2v vector After getting the special velocity object started to move in a parabolic path How far will the ball land from the initial position

4 0 24 m A particle moves along a straight line OX At a time t in seconds the distance x in metres of the particle from O is given by x 40 12t t How long would the particle travel before coming to rest 1 24 m 2 40 m 3 56 m The position 44 16 m

An oblique projectile is projected with a speed u It takes time t to reach maximum height and time t to come back to the ground Air resistance is not t neglected then is t 1 1 2 1 3 1

small wooden sphere of density 0 5 gm cc is attached to centre of the base of the tank with the help of a light inextensible string so that it remains in equilibrium at the centre of tank Now the string is cut and simultaneously the container is given Space for rough work Sec Jr Super60 15 Sri Chaitanya IIT Academy 26 12 2021 Jr Super60 Jee Adv 2019 P2 WTA 18 Q P ahorizontal acceleration 3 along Y axis g 10m s list I is given for different 4 physical quantities and their values are given in list II neglect viscosity and take set of co ordinate axes fixed to container COLUMN I A acceleration of sphere in m s2w r t container B C The y co ordinate in m of the point where the sphere will hit the container for the first time distance travelled by sphere in meters with respect to container before hitting the container for the first time D square of time taken by sphere in s to hit the container for the first time If I b h 1m then which of the following option is correct A AQ BU C V D T P Q R S T U B AQ B S C R D T COLUMN II 2 3 50 4 Page 9 5 8 25197 8 V 1 W 5 6

A train moving with a velocity of 30km hr had to slow down to15 km hr du repairs along the way and then after some time regains its original speed If distance covered during retardation be one km and that during acceleration be km the time lost in the journey is A 3 min B 4 min C 2 min D 1 min

A particle is thrown from a tower height 40 m with initial velocity 20 2 m s making an angle of 45 with horizontal as shown in figure The time at which the particle will strike the ground will be nearest to 40m 1 5 second 45 20 2m s 2 2 3 second

At any instant a projectile is moving with a velocity u in a direction making an angle a to horizon After a certain interval t the direction of its path makes an angle with the horizontal gt tan a tan 3 uwa

A projectile is given an initial velocity 1 2 m s where i is along the ground and is along the vertical If g 10 m s the equation of its trajectory 1 y x 5x2 3 4y 2x 5x 2 y 2x 5x 4 4y 2x 25x

32 A block slides down a rough inclined plane of inclination 300 with a constant speed The value of coefficient of friction between the block and the inclined pane is 0 5 6 3 2 1 3 None of these

nd ABI Example 4 6 Rain is falling vertically with a speed of 35 m s A woman rides a bicycle with a speed of 12 m s in east to west direction What is the direction in which she should hold her umbrella

Two projectiles P and Q are projected simultaneously in vertical X Y plane from same horizontal level as shown in figure The minimum distance between these two projectiles during their motion is 10 m s P O Zero 05m O 10 m O 5 2 m 10m 45 X

A ball projected with velocity from origin m ves in x y plane Ground is taken as x z and g 10 meter per seconds square then 1 Equation of path followed by ball 2 Time of flight 3 Horizontal range of the ball

Katrina and Kareena were crossing a river which is flowing towards right at constant speed 5m min travelling in two different boats having same speed in still water They have taken photographs of the river banks at t 0 t T t 2T times Bo Co are two trees on other bank of river Distance shown in diagram are in m T 1 min Photograph taken by Katrina B B t 0 15 3 15 3 t 0 Bo Photograph taken by Kareena 10 30 B t T 10 3 B t 2T 5 30 1 TC B 5 3 t 2T 0 Mark correct option A Katrina s boat has crossed the river in minimum time and Kareena s boat has crossed the river along the shortest path B Kareena s boat has crossed the river in minimum hos crossed the river along

A particle projected upwards with a velocity U in a medium whose resistance varies as the square of the velocity Prove that the particle will return to the point of projection with velocity UV V after a time tan 1 tanh 1 02 1 g V Wh

A small fish in the sea initially at rest at the origin moves in x y plane with constant acceleration a 27 37 m s It speed in m s after r 1s is O a 11 3 O b 14 4 O c 10 8 O d 3 6 e 7 2

54 A person is standing at 0 a and is observing another person moving with constant velocity v along x axis starting from origin Find at what rate the angular position of the particle is changing with respect to the person 1 V 2a 3a V s later 2 4a M

As a spacecraft moving at 0 92c travels past an observer on Earth the Earthbound observer and the passengers of the craft each start identical alarm clocks that are set to ring after 6 0 hours have passed According to the Earthling what does the Earth clock read when the spacecraft clock rings O 20 hours O 15 hours O 13 hours O 18 hours

A body thrown vertically upward reaches its maximum height in time T The body is at a height h which is less than maximum height at two instants of time t and t Hence product t 1 is given by Imp 1 2 6 4 h g 4h 2 2h g h

A boat travel between two points A and B on the opposite banks of a river figure always following the line AB The distance S between points A and B is 240 m The velocity of the river flow Vr 2 2 m s is constant over the entire width of the river The line AB makes an a 45 with the direction of the current The boat moves to cover the distance AB and back in a time t 2 3 min The angle remains the same during the passage from A to B and from B to A With what velocity u should the boat travel ub a S B

If the acceleration vector of an object is directed parallel to the velocity vector the object is not moving the object is speeding up the object is turning the object is slowing down this situation would not be physically possible Under which of the following conditions would a car have a westward acceleration A a car travels eastward with its velocity is decreasing As a car travels westward with its velocity is decreasing As a car travels eastward with its velocity is constant As a car travels westward with its velocity is constant As a car travels eastward with its velocity is increasing

A small ball is released from position A of a smooth track as shown in figure The height h is adjusted such that the range BC is maximum after leaving the track horizontally where C is point of landing The distance BC in cm is 80 cm 000 00000000 B 0 9 C

Consider a thin layer of liquid of thickness t a cubical block of mass m si ength a is placed over thin layer of liquid as shown in diagram If value orce F to maintain constant velocity vo up the inclined plane is 3mg the Nmgt coefficient of viscosity of liquid is voa find the value of N m 0 37 Vo

0 A massless spring of force constant 1000 N m is compressed a distance of 20 cm between discs of 8 kg and 2 kg spring is not attached to discs The system is given an initial velocity 3 m s perpendicular to length of spring as shown in figure What is ground frame velocity of 2 kg block in m s when spring regains its natural length y B 8kg 2kg A 3m s

3 A block placed at the bottom of rough incline is projected upwards with some initial speed Calculate the retardation of the block while moving up 1 g sine ucos 8 2 g sine ucose 3 g ucos 8 sine 4 g usine cos 54 A particle of mass m moves in a circular path of radius 2m with a speed of 10m s Calculate the time after which the magnitude of change in its momentum becomes equal to its initial momentum 1 sec 15 sec 3 4 Not possible 65 A body starts moving in a straight line under the influence of a variable force F Calculate the time after which the initial velocity of body becomes equal to the final velocity of body for the given F t graph F in N 1 2 2 2 sec 2 SOC t sec sec 2 2 2 sec 2 4 sec

A circuit containing a 80 mH inductor and a 60 F capacitor in series is connected to a 230 V 50 Hz supply The resistance of the circuit is negligible a Obtain the current amplitude and rms values b Obtain the rms values of potential drops across each element What is the average power transferred to the inductor What is the average power transferred to the capacitor What is the total average power absorbed by the circuit Average implies averaged over one cycle 720 19 Suppose the circuit in Exercise 7 18 has a resistance of 15 2 Obtain the average power transferred to each element of the circuit and the total power absorbed

A vessel containing liquid of density po is moving with an acceleration 10 m s n vertical x y plane as shown If the value of PB PA is given by Npo ther ind the value of N PA and Pg are the pressure at A and B g 10 m s AB 10 m 37 In SI

10 2 A projectile is fired with an initial velocity of 800 ft s at a target B located 2000 ft above the gun A and at a horizontal distance of 12 000 ft Neglecting air resistance calculate the value of the firing angle a 800 ft s ja 12 000 ft 2000 ft

A ball is thrown vertically upwards with velo city 15 ms 1 from a top of a building reaches the foot of the building in 5 seconds i Find the height of the building ii with what velocity the ball hits the groun d take g 10 ms 1