Question

At what angle $\left(\theta \right)$ with the horizontal should a body be projected so that its horizontal range equals the maximum height it attains?

• A. $\theta =ta{n}^{-1}\left(\sqrt{2}\right)$
• B. $\theta =ta{n}^{-1}\left(2\sqrt{2}\right)$
• C. $\theta =ta{n}^{-1}\left(2\sqrt{3}\right)$
• D. $\theta =ta{n}^{-1}\left(4\right)$

Answer 1

The correct option is D $\theta =ta{n}^{-1}\left(4\right)$

We know that,

$R=\frac{u^{2}sin2\theta }{g}$ and $h_{max}=\frac{u^{2}sin2\theta }{2g}$

Now according to question, $R=h_{max}$

$\therefore sin2\theta =\frac{si{n}^2\theta }{2}$

or $2sin\theta cos\theta =\frac{si{n}^2\theta }{2}$

$\Rightarrow tan\theta =4$

$\Rightarrow \theta =ta{n}^{-1}\left(4\right)$