The angle of projection of a projectile for which its initial kinetic energy becomes half at its maximum height is (in $^{\circ}$)

$A$ stone is projected in air. Its time of flight is $3\,s$ and range is $150\,m$. The maximum height reached by the stone is $......\,m$ $\left(g=10\,m/s^2\right)$.

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 $45^{\circ}$,its 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:

$A$ ball is thrown upwards at an angle of $60^o$ to the horizontal. It falls on the ground at a distance of $90 \,m$. If the ball is thrown with the same initial velocity at an angle $30^o$,it will fall on the ground at a distance of ........ $m$.

$A$ person can throw a ball up to a maximum range of $100 \, m$. How high above the ground can he throw the same ball (in $, m$)?

$A$ boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give an explanation to support your diagram.