An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be $.......$ degree.

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:

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 :

Derive the formula for time taken to achieve maximum, total time of Flight and maximum height attained by a projectile.

If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to