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Motion in Two Dimensions — JEE Main & Advanced Physics PYQs

336 previous year questions from Motion in Two Dimensions with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

336 questionsPhysicsSolutions on every page
1

A particle is thrown with a speed v from a point O at an angle with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m f

JEE Advanced 2026 Solution View → 2

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum

JEE Main 2026 Solution View → 3

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R . If the time of flight of these bodies are 5 s and 10 s, respectively

JEE Main 2026 Solution View → 4

If x and y coordinates of a projectile as a function of time (t) are given as 24t and 43.6t-4.9t^2 , respectively, then the angle (in degrees) made by the projectile with horizonta

JEE Main 2026 Solution View → 5

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______

JEE Main 2026 Solution View → 6

Two projectiles are projected with the same initial velocities at the 15^ and 30^ with respect to the horizontal. The ratio of their ranges is 1:x . The value of x is:

JEE Main 2026 Solution View → 7

A boy throws a ball into air at 45^ from the horizontal to land it on a roof of a building of height H . If the ball attains maximum height in 2 s and lands on the building in 3 s

JEE Main 2026 Solution View → 8

An object is projected with kinetic energy K from a point A at an angle 60^ with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point

JEE Main 2026 Solution View → 9

A projectile is thrown upward at an angle 60^ with the horizontal. The speed of the projectile is 20 ~m / s when its direction of motion is 45^ with the horizontal. The initial spe

JEE Main 2026 Solution View → 10

A river of width 200 m is flowing from west to east with a speed of 18 ~km / h . A boat, moving with speed of 36 ~km / h in still water, is made to travel one-round trip (bank to b

JEE Main 2026 Solution View → 11

A projectile of mass 200 g is launched in a viscous medium at an angle 60^ with the horizontal, with an initial velocity of 270 ~m / s . It experiences a viscous drag force F =-c v

JEE Advanced 2025 Solution View → 12

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second b

JEE Main 2025 Solution View → 13

Two projectiles are fired from ground with same initial speeds from same point at angles (45^ + ) and (45^ - ) with horizontal direction. The ratio of their times of flights is

JEE Main 2025 Solution View → 14

A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as n u^2 25 g

JEE Main 2025 Solution View → 15

The angle of projection of a particle is measured from the vertical axis as and the maximum height reached by the particle is h_m . Here h_m as function of can be presented as

JEE Main 2025 Solution View → 16

A river is flowing from west to east direction with speed of 9 ~km ~h ⁻¹ . If a boat capable of moving at a maximum speed of 27 ~km ~h ⁻¹ in still water, crosses the river in half

JEE Main 2025 Solution View → 17

Two projectiles are fired with same initial speed from same point on ground at angles of ( (45^ - ) ) and ( (45^ + ) ), respectively, with the horizontal direction. The ratio of th

JEE Main 2025 Solution View → 18

The position vector of a moving body at any instant of time is given as r = (5 t^2 i -5 t j ) m . The magnitude and direction of velocity at t=2 ~s is,

JEE Main 2025 Solution View → 19

A ball of mass 100 g is projected with velocity 20 ~m / s at 60^ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest p

JEE Main 2025 Solution View → 20

A particle is projected at an angle of 30^ from horizontal at a speed of 60 ~m / s . The height traversed by the particle in the first second is h ₀ and height traversed in the las

JEE Main 2025 Solution View → 21

The angle of projection for a projectile to have same horizontal range and maximum height is :

JEE Main 2024 Solution View → 22

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 ~m from the foot of the tower. A body of mass 2 M

JEE Main 2024 Solution View → 23

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 ~m and completes 120 resolutions in 3 minutes. The magnitude of centripetal accelerati

JEE Main 2024 Solution View → 24

The maximum height reached by a projectile is 64 ~m . If the initial velocity is halved, the new maximum height of the projectile is _____ m .

JEE Main 2024 Solution View → 25

The co-ordinates of a particle moving in x-y plane are given by : x=2+4 t , y=3 t +8 t ^2 . The motion of the particle is :

JEE Main 2024 Solution View → 26

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizon

JEE Main 2024 Solution View → 27

A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this perfectly elastic impact, the direction of the velocity of the body

JEE Main 2024 Solution View → 28

Projectiles A and B are thrown at angles of 45 ° and 60 ° with vertical respectively from top of a 400 m high tower. If their times of flight are same, the ratio of their speeds of

JEE Main 2024 Solution View → 29

A particle of mass m projected with a velocity u making an angle of 30 ° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when

JEE Main 2024 Solution View → 30

If the radius of curvature of the path of two particles of same mass are in the ratio 3 : 4 , then in order to have constant centripetal force, their velocities will be in the rati

JEE Main 2024 Solution View → 31

A ball rolls off the top of a stairway with horizontal velocity u . The steps are 0 . 1 m high and 0 . 1 m wide. The minimum velocity u with which that ball just hits the step 5 of

JEE Main 2024 Solution View → 32

A particle of mass m is moving in the x y -plane such that its velocity at a point ( x , y ) is given as v → = α y x ∧ + 2 x y ∧ where α is a non-zero c

JEE Advanced 2023 Solution View → 33

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3 h from the ground, as shown in the figure.

JEE Advanced 2023 Solution View → 34

A person of height 1 . 6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the gro

JEE Advanced 2023 Solution View → 35

A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0 . 2 rad s - 1 . The centripetal force acting on the vehicle is:

JEE Main 2023 Solution View → 36

A disc is rolling without slipping on a surface. The radius of the disc is R . At t = 0 , the top most point on the disc is A as shown in figure. When the disc completes half of it

JEE Main 2023 Solution View → 37

A projectile is projected at 30 ° from horizontal with initial velocity 40 m s - 1 . The velocity of the projectile at t = 2 s from the start will be:

JEE Main 2023 Solution View → 38

A projectile fired at 30 ° to the ground is observed to be at same height at time 3   s and 5   s after projection, during its flight. The speed of projection of the

JEE Main 2023 Solution View → 39

Two projectiles are projected at 30 ° and 60 ° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

JEE Main 2023 Solution View → 40

The range of the projectile projected at an angle of 15 ∘ with horizontal is 50 m . If the projectile is projected with same velocity at an angle of 45 ∘ with horizonta

JEE Main 2023 Solution View → 41

The trajectory of projectile, projected from the ground is given by y = x - x 2 20 . Where x and y are measured in meter. The maximum height attained by the projectile will be.

JEE Main 2023 Solution View → 42

Two projectiles A and B are thrown with initial velocities of 40 m s - 1 and 60 m s - 1 at angles 30 ° and 60 ° with the horizontal respectively. The ratio of their range

JEE Main 2023 Solution View → 43

A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3 . 14 s . The radius of the merry-go-round is 2 m . The centrifugal force on the child will be

JEE Main 2023 Solution View → 44

A particle is moving with constant speed in a circular path. When the particle turns by an angle 90 ° , the ratio of instantaneous velocity to its average velocity is π :

JEE Main 2023 Solution View → 45

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R . Assertion A : When a body is projected at an angle 45 ° , its range is m

JEE Main 2023 Solution View → 46

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 m s – 1 . Neglecting the air resistance, the speed wi

JEE Main 2023 Solution View → 47

A stone of mass 1 kg is tied to end of a massless string of length 1 m . If the breaking tension of the string is 400 N , then maximum linear velocity, the stone can have without b

JEE Main 2023 Solution View → 48

Two bodies are projected from ground with same speeds 40 m s - 1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body wa

JEE Main 2023 Solution View → 49

The initial speed of a projectile fired from ground is u . At the highest point during its motion, the speed of projectile is 3 2 u . The time of flight of the projectile is:

JEE Main 2023 Solution View → 50

The speed of a swimmer is 4 km h - 1 in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km , he reaches a point 750 m down the stream on the op

JEE Main 2023 Solution View → 51

A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936 x m s - 2 . The value of

JEE Main 2023 Solution View → 52

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x = + 2 m , its velocity is - 4 j ^ m s - 1 . The o

JEE Main 2023 Solution View → 53

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to comp

JEE Main 2023 Solution View → 54

A particle of mass 100 g is projected at time t = 0 with a speed 20 m s – 1 at an angle 45 ° to the horizontal as given in the figure. The magnitude of the angular momen

JEE Main 2023 Solution View → 55

A stone is projected at angle 30 ° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will

JEE Main 2023 Solution View → 56

Two objects are projected with same velocity u however at different angles α and β with the horizontal. If α + β = 90 ° , the ratio of horizontal range of

JEE Main 2023 Solution View → 57

A car is moving with a constant speed of 20 m s - 1 in a circular horizontal track of radius 40 m . A bob is suspended from the roof of the car by a massless string. The angle made

JEE Main 2023 Solution View → 58

The maximum vertical height to which a man can throw a ball is 136 m . The maximum horizontal distance upto which he can throw the same ball is

JEE Main 2023 Solution View → 59

A projectile is fired from horizontal ground with speed v and projection angle θ . When the acceleration due to gravity is g , the range of the projectile is d . If at the hig

JEE Advanced 2022 Solution View → 60

A ball is projected with kinetic energy E , at an angle of 60 ° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

JEE Main 2022 Solution View → 61

An object is projected in the air with initial velocity u at an angle θ . The projectile motion is such that the horizontal range R , is maximum. Another object is projected i

JEE Main 2022 Solution View → 62

At time t = 0 a particle starts travelling from a height 7 z ^ cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions a

JEE Main 2022 Solution View → 63

A body of mass 10 kg is projected at an angle of 45 ° with the horizontal. The trajectory of the body is observed to pass through a point 20 , 10 . If T is the time of flight,

JEE Main 2022 Solution View → 64

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle θ with the vertical. Both the balls stay in air for the same period of time. The rati

JEE Main 2022 Solution View → 65

Two projectiles are thrown with same initial velocity making an angle of 45 ° and 30 ° with the horizontal respectively. The ratio of their respective ranges will be

JEE Main 2022 Solution View → 66

Two projectile thrown at 30 ° and 45 ° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

JEE Main 2022 Solution View → 67

If the initial velocity in horizontal direction of a projectile is unit vector i ^ and the equation of trajectory is y = 5 x 1 - x . The y component vector of the initial velocity

JEE Main 2022 Solution View → 68

A ball is projected from the ground with a speed 15 m s - 1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to

JEE Main 2022 Solution View → 69

A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball?

JEE Main 2022 Solution View → 70

A ball is spun with angular acceleration α = 6 t 2 - 2 t where t is in second and α is in rad s - 2 . At t = 0 , the ball has angular velocity of 10 rad s - 1 and angular

JEE Main 2022 Solution View → 71

A projectile is launched at an angle α with the horizontal with a velocity 20 m s - 1 . After 10 s , its inclination with horizontal is β . The value of tan β will b

JEE Main 2022 Solution View → 72

A girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 2 km h - 1 , the rain dro

JEE Main 2022 Solution View → 73

A fighter jet is flying horizontally at a certain altitude with a speed of 200 m s - 1 . When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at a

JEE Main 2022 Solution View → 74

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls A and B thrown with same velocity ' u &#3

JEE Main 2022 Solution View → 75

A body is projected from the ground at an angle of 45 ° with the horizontal. Its velocity after 2 s is 20 m s - 1 . The maximum height reached by the body during its motion is

JEE Main 2022 Solution View → 76

A projectile is projected with velocity of 25 m s - 1 at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizont

JEE Main 2022 Solution View → 77

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum s

JEE Main 2022 Solution View → 78

A projectile is thrown from a point O on the ground at an angle 45^ from the vertical and with a speed 5 2 ~m / s . The projectile at the highest point of its trajectory splits int

JEE Advanced 2021 Solution View → 79

A projectile is thrown from a point O on the ground at an angle 45^ from the vertical and with a speed 5 2 ~m / s . The projectile at the highest point of its trajectory splits int

JEE Advanced 2021 Solution View → 80

The ranges and heights for two projectiles projected with the same initial velocity at angles 42 ° and 48 ° with the horizontal are R 1 , R 2 and H 1 , H 2 respectively.

JEE Main 2021 Solution View → 81

A helicopter is flying horizontally with a speed v at an altitude h has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food

JEE Main 2021 Solution View → 82

A player kicks a football with an initial speed of 25 m s - 1 at an angle of 45 ° from the ground. What are the maximum height and the time taken by the football to reach at t

JEE Main 2021 Solution View → 83

A particle of mass m is suspended from a ceiling through a string of length L . The particle moves in a horizontal circle of radius r such that r = L 2 . The speed of particle will

JEE Main 2021 Solution View → 84

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

JEE Main 2021 Solution View → 85

A swimmer wants to cross a river from point A to point B . Line AB makes an angle of 30 ° with the flow of the river. The magnitude of the velocity of the swimmer is the same

JEE Main 2021 Solution View → 86

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height h at which the block will lose contact with the surface of the sphere is m

JEE Main 2021 Solution View → 87

The water is filled up to a height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth h below the water level. The value of h for which the

JEE Main 2021 Solution View → 88

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t 1 . If he remains stationary on a moving escalator then the es

JEE Main 2021 Solution View → 89

A butterfly is flying with a velocity 4 2 m s - 1 in north-east direction. Wind is slowly blowing at 1 m s - 1 from north to south. The resultant displacement of the butterfly in 3

JEE Main 2021 Solution View → 90

In a spring gun having spring constant 100 N m - 1 a small ball B of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0 . 05 m . There should

JEE Main 2021 Solution View → 91

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : (Take : g = 10 ms - 2

JEE Main 2021 Solution View → 92

The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is 5 2 ms - 1 and the air resistance is assumed to be negligible. The m

JEE Main 2021 Solution View → 93

A person is swimming with a speed of 10 m s - 1 at an angle of 120 ° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the fl

JEE Main 2021 Solution View → 94

A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v . If the coefficient of static friction between the tyres and th

JEE Main 2021 Solution View → 95

A swimmer can swim with velocity of 12   km / h in still water. Water flowing in a river has velocity 6   km / h . The direction with respect to the direction of flow of

JEE Main 2021 Solution View → 96

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm . If the block takes 40 s to complete one round, the norm

JEE Main 2021 Solution View → 97

The trajectory of a projectile in a vertical plane is y = α x - β x 2 , where α and β are constants and x & y are respectively the horizontal and vertical d

JEE Main 2021 Solution View → 98

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5 : 1 . The velocit

JEE Main 2021 Solution View → 99

A particle is projected with velocity v 0 along x -axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. m a = -

JEE Main 2021 Solution View → 100

A uniform electric field, E → = - 400 3 j ^ N C - 1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial spee

JEE Advanced 2020 Solution View → 101

A clock has a continuously moving second's hand of 0 . 1 m length. The average acceleration of the tip of the hand (in units of ms - 2 ]) is of the order of :

JEE Main 2020 Solution View → 102

A bead of mass m stays at point P a , b on a wire bent in the shape of a parabola y = 4 C x 2 and rotating with angular speed ω (see figure). The value of ω is (neglect f

JEE Main 2020 Solution View → 103

A uniform cylinder of mass M and radius R is to be pulled over a step of height a a < R by applying a force F at its centre ' O ' perpendicular to the plane through the

JEE Main 2020 Solution View → 104

A spring mass system (mass m , spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If

JEE Main 2020 Solution View → 105

A particle starts from the origin at t = 0 with an initial velocity of 3.0 i ^ m / s and moves in the x - y plane with a constant acceleration 6.0 i ^ + 4.0 j ^ m / s 2 . The x - c

JEE Main 2020 Solution View → 106

A particle moves such that its position vector r → t = cos ⁡ ω t i ^ + sin ⁡ ω t j ^ where ω is a constant and t is time. Then which of the followi

JEE Main 2020 Solution View → 107

A particle P is projected from a point on the surface of a smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth inclined plane from the s

NTA Abhyas JEE Main 2020 Solution View → 108

Rain droplets are falling in vertically downward direction with velocity 5 m/s . A cyclist is moving in northward direction with velocity 10 m/s . The rain droplets will appear to

NTA Abhyas JEE Main 2020 Solution View → 109

The position vector of a particle is determined by the expression r → = 2 t 2 i ^ + 3 t j ^ + 9 k ^ . The magnitude of its displacement (in m ) in first two seconds is

NTA Abhyas JEE Main 2020 Solution View → 110

A ball is thrown with a speed u , at an angle θ with the horizontal. At the highest point of its motion, the strength of gravity is somehow doubled. Taking this change into account

NTA Abhyas JEE Main 2020 Solution View → 111

A particle is projected from the ground and simultaneously a wedge starts moving towards the right, as shown in the figure. The maximum height of the wedge for which the particle w

NTA Abhyas JEE Main 2020 Solution View → 112

Time taken by the projectile to reach from A to B is t . Then the distance AB is equal to

NTA Abhyas JEE Main 2020 Solution View → 113

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m s - 1 over the hill. The cannon is located at a distance of 80

NTA Abhyas JEE Main 2020 Solution View → 114

Two trains are moving in the same direction along parallel tracks. One of them is 200 m long travelling with a velocity of 20 m s - 1 . The second one is 800 m long travelling with

NTA Abhyas JEE Main 2020 Solution View → 115

Two second after projection a projectile is travelling in a direction inclined at 30 o with horizontal, after one more second it is travelling horizontally. Angle of projection (in

NTA Abhyas JEE Main 2020 Solution View → 116

A particle is projected on a frictionless inclined plane of inclination 37 ° at an angle of projection 45 ° from the inclined plane as shown in the figure. If after the first colli

NTA Abhyas JEE Main 2020 Solution View → 117

A car is travelling at a velocity 10 km h - 1 on a straight road. The driver of the car throws a parcel with a velocity 10 2 km h - 1 with respect to the car, when the car is passi

NTA Abhyas JEE Main 2020 Solution View → 118

Rain drops fall vertically at a speed of 20 m s - 1 . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity 15 m s - 1 , if the wind screen is i

NTA Abhyas JEE Main 2020 Solution View → 119

An inclined plane is located at angle α = 53 ° to the horizontal. There is a hole at point B in the inclined plane as shown in the figure. A particle is projected along the plane w

NTA Abhyas JEE Main 2020 Solution View → 120

A ball is projected with a speed of 2 m s – 1 with respect to a trolley which is moving with 4 m s – 1 , as shown in the figure. The angle at which ball is projected with respect t

NTA Abhyas JEE Main 2020 Solution View →
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