Question

If the maximum range of a projectile is $R$, then the maximum height reached by the projectile is

• A. $R$
• B. $\dfrac{R}{2}$
• C. $\dfrac{R}{3}$
• D. $\dfrac{R}{4}$

Hint:

At $45^\circ$ launch angle, height and range have a defined ratio: $H = \dfrac{R}{4}$.

Answer 1

The Correct Option is D

For a projectile launched at $45^\circ$, the maximum range is given by $R = \dfrac{u^2}{g}$.
The maximum height is given by $H = \dfrac{u^2 \sin^2 \theta}{2g} = \dfrac{u^2}{4g}$ at $\theta = 45^\circ$.
Thus, $H = \dfrac{R}{4}$ since $R = \dfrac{u^2}{g} \Rightarrow u^2 = Rg \Rightarrow H = \dfrac{Rg}{4g} = \dfrac{R}{4}$.