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JEE Motion in Two Dimensions PYQs with Solutions

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

336 questionsPhysics2003–2026Answers + solutions

About Motion in Two Dimensions PYQs

Motion in Two Dimensions has 336 previous year questions in the Quantrex Academy JEE Main & Advanced Physics bank. The 220 questions in this list come from JEE Main (127), NTA Abhyas JEE Main (72), JEE Advanced (20) and 1 other source, spanning 2003 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 10
  • 2025: 10
  • 2024: 11
  • 2023: 27
  • 2022: 19
  • 2021: 22
  • 2020: 79
  • 2019: 13
  • 2018: 2
  • 2017: 1
  • 2014: 4
  • 2013: 4

Motion in Two Dimensions questions with solutions

1

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

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

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

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

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

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

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

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

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

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

JEE Main 2025 Solution View → 13

Two projectiles are fired from ground with same initial speeds from same point at angles (45^ ∘ +α) and (45^ ∘ -α) 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

JEE Main 2025 Solution View → 15

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

JEE Main 2025 Solution View → 17

Two projectiles are fired with same initial speed from same point on ground at angles of \( ( 45^ ^ ∘ - α) \) and \( ( 45^ ^ ∘ + α) \), respectively, with the horizontal

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

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

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

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

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

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 400m 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

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

JEE Main 2024 Solution View → 31

A ball rolls off the top of a stairway with horizontal velocity u . The steps are 0 . 1m high and 0 . 1m 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 xy -plane such that its velocity at a point ( x, y ) is given as → v = α(y ∧ x + 2x ∧ y ) where α is a non-zero constant. What is the force →

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 3h from the ground, as shown in the figure.

JEE Advanced 2023 Solution View → 34

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

JEE Advanced 2023 Solution View → 35

A vehicle of mass 200kg is moving along a levelled curved road of radius 70m with angular velocity of 0 . 2rad 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

JEE Main 2023 Solution View → 37

A projectile is projected at 30 ° from horizontal with initial velocity 40m s ^ - 1 . The velocity of the projectile at t = 2s 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 3s and 5s after projection, during its flight. The speed of projection of the projectile is m s ^

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 50m . If the projectile is projected with same velocity at an angle of 45 ^ ∘ with horizontal, then

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 40m s ^ - 1 and 60m s ^ - 1 at angles 30 ° and 60 ° with the horizontal respectively. The ratio of their ranges

JEE Main 2023 Solution View → 43

A child of mass 5kg is going round a merry-go-round that makes 1 rotation in 3 . 14s . The radius of the merry-go-round is 2m . 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: x 2 . The

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

JEE Main 2023 Solution View → 46

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

JEE Main 2023 Solution View → 47

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

JEE Main 2023 Solution View → 48

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

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

JEE Main 2023 Solution View → 51

A stone tied to 180cm 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

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 = + 2m , its velocity is - 4 ^ j m s ^ - 1 . The

JEE Main 2023 Solution View → 53

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

JEE Main 2023 Solution View → 54

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

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 be :

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 the first object to the

JEE Main 2023 Solution View → 57

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

JEE Main 2023 Solution View → 58

The maximum vertical height to which a man can throw a ball is 136m . 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 highest

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 in

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

JEE Main 2022 Solution View → 63

A body of mass 10kg 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 2m is thrown an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of

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 = 5x(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 ms ^ - 1 at an angle θ with horizontal so that its range and maximum height are equal, then tanθ will be equal to

JEE Main 2022 Solution View → 69

A person can throw a ball upto a maximum range of 100m . 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 - 2t where t is in second and α is in rad s ^ - 2 . At t = 0 , the ball has angular velocity of 10rad 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 ms ^ - 1 . After 10s , its inclination with horizontal is β . The value of tanβ will be : (g = 10 ms

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 drops

JEE Main 2022 Solution View → 73

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

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

JEE Main 2022 Solution View → 75

A body is projected from the ground at an angle of 45 ° with the horizontal. Its velocity after 2s is 20 ms ^ - 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 25m s ^ - 1 at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal

JEE Main 2022 Solution View → 77

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

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

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

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

JEE Main 2021 Solution View → 82

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

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

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 as

JEE Main 2021 Solution View → 86

A small block slides down from the top of hemisphere of radius R = 3m 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 12m 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

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 1m s ^ - 1 from north to south. The resultant displacement of the butterfly

JEE Main 2021 Solution View → 90

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

JEE Main 2021 Solution View → 92

The projectile motion of a particle of mass 5g 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

JEE Main 2021 Solution View → 93

A person is swimming with a speed of 10m 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 flow

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

JEE Main 2021 Solution View → 95

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

JEE Main 2021 Solution View → 96

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

JEE Main 2021 Solution View → 97

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

JEE Main 2021 Solution View → 98

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

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. ma =

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

JEE Advanced 2020 Solution View → 101

A clock has a continuously moving second's hand of 0 . 1m 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 = 4C x ^ 2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction)

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

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

JEE Main 2020 Solution View → 106

A particle moves such that its position vector → r (t) = cos ⁡ ^ i + sin ⁡ ^ j where ω is a constant and t is time. Then which of the following statements is true for the velocity

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

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 = 2t^ 2 ^ i + 3t ^ 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

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

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

NTA Abhyas JEE Main 2020 Solution View → 114

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

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

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

NTA Abhyas JEE Main 2020 Solution View → 117

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

NTA Abhyas JEE Main 2020 Solution View → 118

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

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

NTA Abhyas JEE Main 2020 Solution View → 120

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

NTA Abhyas JEE Main 2020 Solution View →
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