A projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

If a body $A$ of mass $M$ is thrown with velocity $v$ at an angle of ${30^o}$ to the horizontal and another body $B$ of the same mass is thrown with the same speed at an angle of ${60^o}$ to the horizontal. The ratio of horizontal range of $A$ to $B$ will be

A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2s$ is $20 \,ms ^{-1}$. The maximum height reached by the body during its motion is $m$. (use $g =10\, ms ^{-2}$ )

At the top of the trajectory of a projectile, the directions of its velocity and acceleration are

A projectile has the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the times of flight in the two cases, then $R$ is