Question

The equation of motion of a projectile are $x=36t$ and $2y=96t-9.8t^2$. Angle of projection is ;-

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

Answer 1

The correct option is A ${\sin }^{-1}\left(\frac{4}{5}\right)$

Putting $t=\frac{36}{x}$ in the expression of $y$ we get $y=\frac{48x}{36}-x^2\frac{9.8}{36\times 36}$

Comparing it with the standard equation, $y=xtan\theta -\frac{g{x}^2}{u^{2}Co{s}^2\theta }$

We get $tan\theta =\frac{4}{3}$ so $Sin\theta =\frac{4}{\sqrt[2]{23^2+4^4}}$ or $\theta =si{n}^{-1}\frac{4}{5}$

option A is correct.