Motion in a Plane · Physics · JEE Main

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

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...

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....

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 ...

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

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...

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...

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...

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...

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...

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}^...

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...

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

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 :...

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...

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

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

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...

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...

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...

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

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 '$$\...

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...

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...

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 ...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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 ...

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...

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. ...

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...

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...

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...

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...

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...

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...

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...

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 ...

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...

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...

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...

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

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...

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...

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:

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...

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...

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...

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 ...

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...

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 _____...

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...

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...

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, ...

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...

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 $$...

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...

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...

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 $$y$$...

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...

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 ...

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 ...

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...

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 ...

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 ...