Kinematics — JEE Advanced PYQs

A particle is thrown with a speed $v$ from a point $O$ at an angle $\theta$ with the horizontal plane such that it passes through the point $P$ at a height of 1 m and horizontal distance of 5 m from $O$, as shown in the figure. If acceleration due to gravity is …

A ball is thrown from the location $\left({\mathrm{x}}_0,{\mathrm{y}}_0\right)=(0,0)$ 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 the location …

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. A spherical ball of mass m is released on the slide from rest at a height $h$ from the top of the t …

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 ground. If the speed of the person is $60\mathrm{cm}{\mathrm{s}}^{-1}$, the speed of the tip of the per …

A particle of mass m is moving in the $xy$-plane such that its velocity at a point $(x,y)$ is given as $\vec{v}=\alpha (y\hat{x}+2x\hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

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 different region where the effect …

List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. List II gives possible magnitudes of their relative velocities (in $m{s}^{-1}$) at time $t=\frac{\pi }{3}s$.
| (I) …

Starting at time $t=0$ from the origin with speed $1{\text{ ms}}^{-1}$, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $y=\frac{x^2}{2}$. The x and y components of its acceleration are denoted by $a_x$ and …

A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed ${\mathrm{u}}_0$. 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 is ${\mathrm{V}}_1$. A …

A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of $120m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of t …

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 …

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and $60^{\circ }$ with respect to the horizontal respectively as shown in figure. The speed of A is $100\sqrt{3}m{s}^{-1}$. At time $t=0s$, an observer in A finds B at a distance o …

A rocket is moving in a gravity free space with a constant acceleration of $2m{s}^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of …

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at $t=0$. It then execute …

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$, the points $P$ and $Q$ are facing each other as shown in the figure. The …

Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase …

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.
and
STATEMENT-2
If the observer and the object are moving at velocities …