Question

The maximum range of a projectile fired with some initial velocity is found to be $1000$ meter. The maximum height $\left(H\right)$ reached by this projectile is:

• A. $250$ metre
• B. $500$ metre
• C. $1000$ metre
• D. $2000$ metre

Answer 1

The correct option is A $250$ metre

Let the projectile velocity be $u$ and the angle of projection with horizontal be $\theta$.

As the range of the particle is maximum $⟹\theta ={45}^o$

Maximum horizontal range $R_{max}=\frac{u^2}{g}=1000$ m

Maximum height $H=\frac{u^{2}si{n}^2\left({45}^o\right)}{2g}=\frac{u^2}{4g}$ $\left[si{n}^2\right({45}^o)=0.5]$

$⟹$ $H=\frac{R_{max}}{4}=\frac{1000}{4}=250$ m