# Motion in a Plane · Physics · JEE Main

Start Practice## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 8th April Evening Shift

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

JEE Main 2024 (Online) 4th April Morning Shift

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

JEE Main 2024 (Online) 30th January Evening Shift

Projectiles A and B are thrown at angles of $$45^{\circ}$$ and $$60^{\circ}$$ with vertical respectively from top of a $$400 \mathrm{~m}$$ high tower....

JEE Main 2024 (Online) 27th January Morning Shift

Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2 t^2 \hat{j}+5 \hat{k}$$ (where $$t$$ is ...

JEE Main 2023 (Online) 11th April Evening Shift

A projectile is projected at $$30^{\circ}$$ from horizontal with initial velocity $$40 \mathrm{~ms}^{-1}$$. The velocity of the projectile at $$\mathr...

JEE Main 2023 (Online) 10th April Evening Shift

Two projectiles are projected at $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal with the same speed. The ratio of the maximum height attained b...

JEE Main 2023 (Online) 10th April Morning Shift

The range of the projectile projected at an angle of 15$$^\circ$$ with horizontal is 50 m. If the projectile is projected with same velocity at an ang...

JEE Main 2023 (Online) 8th April Evening Shift

The trajectory of projectile, projected from the ground is given by $$y=x-\frac{x^{2}}{20}$$. Where $$x$$ and $$y$$ are measured in meter. The maximum...

JEE Main 2023 (Online) 8th April Morning Shift

Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\cir...

JEE Main 2023 (Online) 6th April Morning Shift

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 ang...

JEE Main 2023 (Online) 1st February Morning Shift

A child stands on the edge of the cliff $$10 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initial speed of $$5 \mathrm{~ms}^...

JEE Main 2023 (Online) 31st January Morning Shift

The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed of projectile is $$\frac{\sqr...

JEE Main 2023 (Online) 25th January Evening Shift

Two objects are projected with same velocity 'u' however at different angles $$\alpha$$ and $$\beta$$ with the horizontal. If $$\alpha+\beta=90^\circ$...

JEE Main 2023 (Online) 24th January Morning Shift

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 2022 (Online) 28th July Evening Shift

At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate constant. At any instant of time...

JEE Main 2022 (Online) 26th July Evening Shift

Two projectiles are thrown with same initial velocity making an angle of $$45^{\circ}$$ and $$30^{\circ}$$ with the horizontal respectively. The rati...

JEE Main 2022 (Online) 26th July Morning Shift

Two projectiles thrown at $$30^{\circ}$$ and $$45^{\circ}$$ with the horizontal respectively, reach the maximum height in same time. The ratio of thei...

JEE Main 2022 (Online) 25th July Evening Shift

A ball is projected from the ground with a speed 15 ms$$-$$1 at an angle $$\theta$$ with horizontal so that its range and maximum height are equal, th...

JEE Main 2022 (Online) 30th June Morning Shift

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms$$-$$2. At t = 20 s, a ball is released from the...

JEE Main 2022 (Online) 30th June Morning Shift

Two projectiles P1 and P2 thrown with speed in the ratio $$\sqrt3$$ : $$\sqrt2$$, attain the same height during their motion. If P2 is thrown at an an...

JEE Main 2022 (Online) 29th June Evening Shift

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 (Online) 27th June Morning Shift

A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms$$-$$1. After 10 s, its inclination with horizontal is '$$\...

JEE Main 2022 (Online) 27th June Morning Shift

A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts running without umbrella with a spee...

JEE Main 2022 (Online) 25th June Evening Shift

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...

JEE Main 2022 (Online) 24th June Morning Shift

A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclination with horizontal becomes ...

JEE Main 2021 (Online) 1st September Evening Shift

The ranges and heights for two projectiles projected with the same initial velocity at angles 42$$^\circ$$ and 48$$^\circ$$ with the horizontal are R1...

JEE Main 2021 (Online) 31st August Morning Shift

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 hel...

JEE Main 2021 (Online) 27th August Evening Shift

A player kicks a football with an initial speed of 25 ms$$-$$1 at an angle of 45$$^\circ$$ from the ground. What are the maximum height and the time t...

JEE Main 2021 (Online) 26th August Evening Shift

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

JEE Main 2021 (Online) 20th July Morning Shift

A butterfly is flying with a velocity $$4\sqrt 2 $$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant di...

JEE Main 2021 (Online) 16th March Evening Shift

A mosquito is moving with a velocity $$\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$$ m/s and accelerating in uniform conditio...

JEE Main 2021 (Online) 26th February Evening Shift

The trajectory of a projectile in a vertical plane is y = $$\alpha$$x $$-$$ $$\beta$$x2, where $$\alpha$$ and $$\beta$$ are constants and x & y ar...

JEE Main 2020 (Online) 6th September Evening Slot

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with
speed v, he sees that rain drops are coming at a...

JEE Main 2020 (Online) 5th September Morning Slot

A balloon is moving up in air vertically above a
point A on the ground. When it is at a height h1,
a girl standing at a distanced (point B) from A
(se...

JEE Main 2020 (Online) 4th September Morning Slot

Starting from the origin at time t = 0, with initial velocity 5$$\widehat j$$ ms-1 , a particle moves in the x-y plane
with a constant acceleration of...

JEE Main 2020 (Online) 9th January Evening Slot

A particle starts from the origin at t = 0 with an
initial velocity of 3.0 $$\widehat i$$ m/s and moves in the
x-y plane with a constant acceleration
...

JEE Main 2020 (Online) 8th January Evening Slot

A particle moves such that its position
vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\ome...

JEE Main 2019 (Online) 12th April Evening Slot

Two particles are projected from the same point with the same speed u such that they have the same range R,
but different maximum heights, h1 and h2. ...

JEE Main 2019 (Online) 12th April Morning Slot

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a
distance R from it. If t1 and t2 a...

JEE Main 2019 (Online) 12th April Morning Slot

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2
. If it were launched at an
angle $$\theta $$0 with speed v0 the...

JEE Main 2019 (Online) 10th April Evening Slot

A plane is inclined at an angle $$\alpha $$ = 30° with respect to the horizontal. A particle is projected with a speed u =
2 ms–1
, from the base of t...

JEE Main 2019 (Online) 9th April Morning Slot

The stream of a river is flowing with a speed
of 2km/h. A swimmer can swim at a speed of
4km/h. What should be the direction of the
swimmer with respe...

JEE Main 2019 (Online) 8th April Morning Slot

Ship A is sailing towards north-east with
velocity $$\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge $$ km/hr whe...

JEE Main 2019 (Online) 12th January Morning Slot

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplan...

JEE Main 2019 (Online) 10th January Morning Slot

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible direct...

JEE Main 2019 (Online) 9th January Evening Slot

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos$$\omega $$t
y = a sin$$\omega $$t and
z = a$$\omega ...

JEE Main 2019 (Online) 9th January Morning Slot

A particle is moving with a velocity
$$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant.
The general equation for its pat...

JEE Main 2018 (Online) 15th April Evening Slot

A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in a field at a distance d from t...

JEE Main 2013 (Offline)

A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\wid...

AIEEE 2012

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy
can throw the same stone up to will be

AIEEE 2011

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the
fountain is v, the total area around the fountai...

AIEEE 2010

A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a constant. The general equation f...

AIEEE 2009

A particle has an initial velocity $$3\widehat i + 4\widehat j$$ and an acceleration of $$0.4\widehat i + 0.3\widehat j$$. Its speed after 10 s is:

AIEEE 2005

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity
changes to 5 m/s northwards. The average acceleration in this time...

AIEEE 2004

A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time
of flights in the two cases, then the product of the t...

AIEEE 2004

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point
and at the same instant person starts running with a co...

AIEEE 2003

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an
angle of $$30^\circ $$ with the horizontal. How far from ...

## Numerical

JEE Main 2024 (Online) 8th April Evening Shift

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 $$100 \mathrm{~m}$$ fro...

JEE Main 2024 (Online) 5th April Evening Shift

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

JEE Main 2024 (Online) 29th January Morning Shift

A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimu...

JEE Main 2024 (Online) 27th January Morning Shift

A particle starts from origin at $$t=0$$ with a velocity $$5 \hat{i} \mathrm{~m} / \mathrm{s}$$ and moves in $$x-y$$ plane under action of a force whi...

JEE Main 2023 (Online) 11th April Morning Shift

A projectile fired at $$30^{\circ}$$ to the ground is observed to be at same height at time $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ after projection, ...

JEE Main 2023 (Online) 31st January Evening Shift

Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The bodies were found...

JEE Main 2023 (Online) 31st January Morning Shift

The speed of a swimmer is $$4 \mathrm{~km} \mathrm{~h}^{-1}$$ in still water. If the swimmer makes his strokes normal to the flow of river of width $$...

JEE Main 2022 (Online) 29th July Morning Shift

An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the horizontal range R, is maximu...

JEE Main 2022 (Online) 27th July Morning Shift

A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ with the vertical. Both the ball...

JEE Main 2022 (Online) 26th July Morning Shift

If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y=5 x(1-x)$$. The $$y$$...

JEE Main 2022 (Online) 26th June Morning Shift

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 bull...

JEE Main 2022 (Online) 24th June Evening Shift

A body is projected from the ground at an angle of 45$$^\circ$$ with the horizontal. Its velocity after 2s is 20 ms$$-$$1. The maximum height reached ...

JEE Main 2021 (Online) 27th July Evening Shift

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river. Magnitude of velocity of the ...

JEE Main 2021 (Online) 18th March Morning Shift

A person is swimming with a speed of 10 m/s at an angle of 120$$^\circ$$ with the flow and reaches to a point directly opposite on the other side of t...

JEE Main 2021 (Online) 16th March Evening Shift

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 ...

JEE Main 2020 (Online) 8th January Morning Slot

A particle is moving along the x-axis with its
coordinate with the time 't' given be x(t) = 10 + 8t – 3t2. Another particle is moving
the y-axis with ...