Motion

A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from ...

A person of height $1.6 \mathrm{~m}$ is walking away from a lamp post of height $4 \mathrm{~m}$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60...

A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a d...

Starting at time t = 0 from the origin with speed 1 ms-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation \(y = {{{x^2}} \over 2}\). The x and y components of its accelera...

A ball is thrown from ground at an angle \(\theta\) with horizontal and with an initial speed u0. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time...

A ball is projected from the ground at an angle of \({45^o}\) with the horizontal surface. It reaches a maximum height of \(120\) \(m\) and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic ener...

Three vectors \(\overrightarrow P ,\overrightarrow Q\) and \(\overrightarrow R\) are shown in the figure. Let \(S\) be any point on the vector \(\overrightarrow R .\) The distance between the points \(P\) and \(S\) is $$b\left| {\overrig...

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density \(\rho\) remains uniform throughout the volume. The rate of fractional change in density $$\left...

A rocket is moving in a gravity free space with a constant
acceleration of 2 ms–2 along + x direction (see figure). The
length of a chamber inside the rocket is 4 m. A ball is
thrown from the left end of the chamber in + x direction
with a ...

Airplanes A and B are flying with constant velocity in the same vertical plane at angles \(30^\circ\) and \(60^\circ\) with
respect to the horizontal respectively as shown in the figure. The speed of A is \(100\sqrt 3\) m/s. At time t = ...

A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at an angle of \(60^\circ\) to the horizontal. The boy has to move forward by
1.15 m inside...

STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the
opposite direction to the train, while the distant objects appear to be stationary.
STATEMENT-2: If the observer an...

While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is :

A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio Sn / Sn+1 is

A body starts from rest at time t = 0, the acceleration time graph is
shown in the figure. The maximum velocity attained by the body
will be

The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of approprite dimensions. Then

Two guns, situated on the top of a hill of height 10 m, fire one shot each with the same speed \(5\sqrt 3\) m s-1 at some interval of time. One gun fires horizontally and other fires upwards at an angle of \(60^\circ\) with the horizontal...

A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If...

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails.

A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.

Four person K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly to...

Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (Neglect air resistance)

A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance covered is _________.

A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of swimming at 10 meters per minute in still water, wants to swim across the river in the shortest time. He should swim in...

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

The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation \(t = \sqrt x + 3\)
where x is in meters and t in seconds. Find
(i) The displacement of the particle when...

Answer the following giving reason in brief:
Is the time variation of position, shown in the figure observed in nature?

A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time lapse is t seconds, evaluate.
(i) maximum velocity reached, and
(ii) the to...