Question

The maximum range of a projectile fired with some initial velocity is found to be $1000$ metre. The maximum height (H) 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

Range of projectile R= $\frac{{\text{u}}^2\text{sin2}\theta }{\text{2g}}$---- (1)

For maximum height, angle of projection should be ${45}^o$

Maximum height, H=$\frac{{\text{u}}^2{\text{sin}}^2\theta }{\text{2g}}$---- (2)

(2)$÷$ (1) = $\frac{\left(\frac{{\text{u}}^2{\text{sin}}^2\theta }{\text{2g}}\right)}{\left(\frac{{\text{u}}^2\text{sin2}\theta }{\text{g}}\right)}$

=$\frac{{\text{sin}}^2\theta }{\text{2Sin2}\theta }$

=$\frac{\text{H}}{\text{R}}=\frac{1}{4}$

H=R$\times \frac{1}{4}$

Since R= $1000m$

H = $250m$