An object is thrown along a direction inclined at an angle of ${45^o}$ with the horizontal direction. The horizontal range of the particle is equal to

Shots are fired from the top of a tower and from its bottom simultaneously at angles $30^o$ and $60^o$ as shown. If horizontal distance of the point of collision is at a distance $'a'$ from the tower then height of tower $h$ is :

A boy can throw a stone up to a maximum height of $10\ m$. The maximum horizontal distance that the boy can throw the same stone up to will be ..........  $m$

At what angle of elevation, should a projectile be projected with velocity $20 \,ms ^{-1}$, so as to reach a maximum height of $10 \,m$ ?

A cricket fielder can throw the 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 air as seen by a spectator

$(b)$ what will be time of flight?

$(c)$ what is the distance (horizontal range) from the point of projection at which the ball will land ?

$(d)$ find $\theta$ at which he should throw the ball that would maximise the horizontal range as  found in $(iii)$.

$(e)$ how does $\theta $ for maximum range change if $u > u_0$. $u =u_0$ $u < v_0$ ?

$(f)$ how does $\theta $ in $(v)$ compare with that for $u=0$ $($ i.e., $45^{o})$ ?

The speed of a projectile at its maximum height is $\frac {\sqrt 3}{2}$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it, $P$ is equal to