Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

A body is projected with velocity $u$ making an angle $\alpha$ with the horizontal. Its velocity when it is perpendicular to the initial velocity vector $u$ is

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is ......... $^o$

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

The velocity of projectile at the intial point $A$ is $\left( {2\hat i + 3\hat j} \right)$ $m/s $ . It's velocity (in $m/s$) at point $B$ is

A cricket ball is thrown by a player at a speed of $20\,m / s$ in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is $........\,m$ $\left( g =10\,m / s ^2\right)$