A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

A spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released the spring exerts equal and opposite forces for the same time $t$ on each toy cart. If the coefficients of friction $\mu $ between the ground and the toy carts are equal, then the displacement of the toy carts are in the ratio

A stationary particle explodes into two particles of a masses $m_1$ and $m_2$ which move in opposite directions with velocities ${v_1}$ and ${v_2}.$ The ratio of their kinetic energies ${E_1}/{E_2}$ is

particle is projected from level ground. Its kinetic energy $K$ changes due to gravity so $\frac{{{K_{\max }}}}{{{K_{\min }}}} = 9$. The ratio of the range to the maximum height attained during its flight is

$A$ ball is projected vertically upwards. Air resistance  variation in $g$ may be neglected. The ball rises to its maximum height $H$ in a time $T$, the height being $h$ after a time $t$

$[1]$ The graph of kinetic energy $E_k$ of the ball against height $h$ is shown in figure $1$

$[2]$ The graph of height $h$ against time $t$ is shown in figure $2$

$[3]$ The graph of gravitational energy $E_g$ of the ball against height $h$ is shown in figure $3$

Which of $A, B, C, D, E$ shows the correct answers?