Question

A body is projected with velocity $24m{s}^{-1}$ making an angle ${30}^{\circ }$ with the horizontal. The angle made by the direction of the projectile with the horizontal at $2s$ from start is:

• A. ${\tan }^{-1}\frac{2}{3\sqrt{3}}$
• B. ${\tan }^{-1}\frac{1}{3\sqrt{3}}$
• C. ${\tan }^{-1}\frac{2}{3}$
• D. ${\tan }^{-1}\frac{1}{3}$

Answer 1

The correct option is A ${\tan }^{-1}\frac{2}{3\sqrt{3}}$

Given,

$u=24m/s$

$\theta ={30}^0$

Take, $g=10m/s^2$

lets consider $\varphi$ the angle made by the direction of projectile with the horizontal at $2s$ from start

$tan\varphi =\frac{usin\theta +gt}{ucos\theta }$

$tan\varphi =\frac{24\times sin30+(-10)\times 2}{24\times cos30}$

$tan\varphi =\frac{-8}{12\sqrt{3}}$

$tan\varphi =-\frac{2}{3\sqrt{3}}$

$\varphi =-ta{n}^{-1}\left(\frac{2}{3\sqrt{3}}\right)$, ($tan\varphi =-tan\varphi$)

The correct option is A.