$A$ ball is thrown horizontally from a height with a certain initial velocity at time $t=0$. The ball bounces repeatedly from the ground with the coefficient of restitution less than $1$ as shown below. Neglecting air resistance and taking the upward direction as positive,which figure qualitatively depicts the vertical component of the ball's velocity $v_y$ as a function of time $t$?

$A$ ball is projected from the ground at an angle of $45^{\circ}$ 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 energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is.

If the radius of the circular path and the frequency of revolution of a particle of mass $m$ are doubled,then the change in its kinetic energy will be ($E_i$ and $E_f$ are the initial and final kinetic energies of the particle respectively). (in $E_i$)

$A$ car starts from rest and accelerates at $5 \, m/s^{2}$. At $t=4 \, s$,a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6 \, s$? (Take $g = 10 \, m/s^{2}$)

$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

$A$ boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $f_a$ cannot be ignored,the forces acting on the ball at the position $X$ are represented by