Question

The horizontal range of a projectile is $400\, m$. The maximum height attained by it will be:

• A. 100 m
• B. 200 m
• C. 400 m
• D. 800 m

Answer 1

Answer: (A)

100 m

Answer 2

In order to obtain maximum range the body should be projected at an angle of $45^{\circ}$. Horizontal range = horizontal velocity $\times$ time $H =$ Height $R =$ Range $R=u_{x} \times T$ $R=(u \cos \theta) \times \frac{2 u \sin \theta}{g}$ $R=\frac{u^{2} 2 \sin \theta \cos \theta}{g}$ $R=\frac{u^{2} \sin 2 \theta}{g}$ For maximum horizontal range, $2 \sin 2 \theta=1$ $\therefore \theta=45^{\circ}$ $\therefore 400=\frac{u^{2}}{g}$ ...(i) Also, maximum height of projectile is $H=\frac{u^{2} \sin ^{2} \theta}{2 g}=\frac{u^{2} \sin ^{2} 45^{\circ}}{2 g}$ $=\frac{400}{2} \times \frac{1}{2}=100\, m$