Question

A boy projects a stone vertically perpendicular to the trolley car with a speed $v$. If the trolley car moves with a constant velocity $u$. The angle of projection relative to horizontal is:

• A. ${\tan }^{-1}\frac{v}{u}$
• B. ${\tan }^{-1}\frac{u}{v}$
• C. ${\sin }^{-1}\frac{v}{u}$
• D. ${\sin }^{-1}\frac{u}{v}$

Answer 1

The correct option is A ${\tan }^{-1}\frac{v}{u}$

Resolve the velocity of projection $v_o$ into horizontal and vertical component.

$v_0\sin \theta =v\dots \left(i\right)$
$v_0\cos \theta =u\dots \left(ii\right)$

From equations $\left(i\right)$ and $\left(ii\right)$,

Angle of projection with horizontal,
$\tan \theta =\frac{v}{u}$

$\theta ={\tan }^{-1}\left(\frac{v}{u}\right)$