On which does the value of range depend ? On which does the maximum value of range depend ?

Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long-jump event

Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : When a body is projected at an angle $45^{\circ}$, it's range is maximum.

Reason $R$ : For maximum range, the value of $\sin 2 \theta$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below :

A stone is projected from the ground with velocity $50 \,m/s$ at an angle of ${30^o}$. It crosses a wall after $3$ sec. How far beyond the wall the stone will strike the ground ..........  $m$ $(g = 10\,m/{\sec ^2})$

A cricketer can throw a ball to a maximum horizontal distance of $100\, m$. The speed with which he throws the ball is   ......... $ms^{-1}$ (to the nearest integer)

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