A mouse is at a distance of $d$ from a cat. Both start running with constant equal speed $v_0$ in such a way that mouse moves in a straight line perpendicular to initial line joining cat and mouse, and cat always moves aiming at mouse. Separation between them when both move on the same line is

A particle is moving in $X-Y$ plane on path $y=x^2-$ $2x+5.$ Its $x$ component of velocity is constant and is equal to $5 \mathrm{m} {\mathrm{s}}^{-1}.$ Acceleration of the particle at $x=2 \mathrm{m}$ is

The figure shows three paths for a ball projected from ground level. Ignore the effects of air on flight. Which of the following statements is correct?

Figure shows the path of a projectile thrown near the surface of earth in the absence of air resistance.

If the air resistance is taken into consideration, then

A ball is thrown with velocity $\overrightarrow{u}=(3\hat{i}+4\hat{j})\mathrm{m} {\mathrm{s}}^{-1}$ towards a wall, where it hits at height $h_1$ at time $t_1$ after the launch.

Another ball is projected from same point with velocity $\overrightarrow{u}=(3\hat{i}+5\hat{j})\mathrm{m} {\mathrm{s}}^{-1}$ towards the wall where it hits at height $h_2$ at time $t_2$ after the launch. Then