Question

The equation of motion of a projectile are given by $x=36t$ metre and $2y=96t-9.8t^2$ metre. The angle of projection is-

• A. $si{n}^{-1}\left(\frac{4}{5}\right)$
• B. $si{n}^{-1}\left(\frac{3}{5}\right)$
• C. $si{n}^{-1}\left(\frac{4}{3}\right)$
• D. $si{n}^{-1}\left(\frac{3}{4}\right)$

Answer 1

Answer: (A)

$si{n}^{-1}\left(\frac{4}{5}\right)$

$x=ucos\theta t=36t$

$s=ut+\frac{1}{2}a{t}^2$

$2s=2usin\theta t-g{t}^2$

therefore $2usin\theta =96$

therefore $tan\theta =\frac{usin\theta }{ucos\theta }=\frac{48}{36}=\frac{4}{3}$

$⟹\theta =si{n}^{-1}\left(\frac{4}{5}\right)$