A small boy is throwing a ball towards a wall $6 \,m$ in front of him. He releases the ball at a height of $1.4 \,m$ from the ground. The ball bounces from the wall at a height of $3 \,m$, rebounds from the ground and reaches the boy's hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic, ………. $m$ far ahead of the boy did the ball bounce from the ground

There are two points $P$ and $Q$ on a projectile with velocities $v_P$ and $v_Q$ respectively such that $v_P$ is perpendicular to $v_Q$ and $\alpha$ is the angle that $v_P$ makes with horizontal at point $P$. Find the correct option

The maximum horizontal range of a projectile is $400\, m$. The maximum value of height attained by it will be    ……… $m$

The trajectory of a projectile near the surface of the earth is given as$ y = 2x -9x^2$. If it were launched at an angle $\theta_0$ with speed $v_0$ then $(g = 10\, ms^{-2}$)