$A$ ball is projected with kinetic energy $E$, at an angle of $60^{\circ}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will be:

$A$ batsman hits a ball with a velocity '$v$',making an angle of $60^{\circ}$ with the vertical. After some time, the direction of velocity makes an angle of $60^{\circ}$ with the horizontal. The speed of the ball at this instant is $[\cos(60^{\circ}) = \frac{1}{2}, \cos(30^{\circ}) = \frac{\sqrt{3}}{2}]$.

$A$ cricket fielder can throw a cricket ball with a speed $v_{0}$. If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal,find:
$(a)$ The effective angle to the horizontal at which the ball is projected in the air as seen by a spectator.
$(b)$ The time of flight.
$(c)$ The horizontal range from the point of projection at which the ball will land.
$(d)$ The angle $\theta$ at which he should throw the ball to maximize the horizontal range found in $(c)$.
$(e)$ How does $\theta$ for maximum range change if $u > v_{0}$,$u = v_{0}$,and $u < v_{0}$?
$(f)$ How does $\theta$ in $(e)$ compare with that for $u = 0$ (i.e.,$45^{\circ}$)?

$A$ boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved $100 \,m$. If the truck is moving horizontally along a straight line with a constant speed $30 \,m/s$, at what speed (relative to the truck) must the projectile be thrown? (Assume $g = 10 \,m/s^2$)

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

The angle of projection for a projectile to have the same horizontal range and maximum height is