Motion PYQs - Last 10 Years

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...