Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

The mass of a person is $60 \, kg$. If he gains $10^5 \, \text{calories}$ of heat energy from food and the efficiency of his body is $28 \%$,then up to what height can he climb? (approximately) ($g = 9.8 \, m/s^2$,$J = 4.2 \, J/\text{cal}$)

$A$ sphere of mass $m$ slides down a smooth inclined plane from a point $B$ at a height of $h$ starting from rest. The magnitude of the change in momentum of the particle between position $A$ (at the bottom of the incline) and $C$ (on the horizontal surface) is (assuming the angle of inclination of the plane is $\theta$ with respect to the horizontal):

$A$ body is moved from rest along a straight line by a machine delivering constant power. The ratio of displacement and velocity $(s/v)$ varies with time $t$ as :

$A$ block of mass $1\,kg$ is pushed up a surface inclined to the horizontal at an angle of $30^{\circ}$ by a force of $10\,N$ parallel to the inclined surface (see figure). The coefficient of friction between the block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the incline,calculate:
$(a)$ Work done against gravity
$(b)$ Work done against the force of friction
$(c)$ Increase in potential energy
$(d)$ Increase in kinetic energy
$(e)$ Work done by the applied force

In a one-dimensional collision between two particles,their relative velocity is $\vec{v}_1$ before the collision and $\vec{v}_2$ after the collision.