Question

A ball is projected with a speed of $2m{s}^{-1}$ with respect to a trolley which is moving with $4m{s}^{-1}$ as shown. The angle at Which ball is proejcted with respect to the horizontal in ground frame is

diagram

• A. ${\tan }^{-1}\left(\frac{5}{\sqrt{3}}\right)$
• B. ${\sin }^{-1}\left(\frac{5}{\sqrt{28}}\right)$
• C. ${\tan }^{-1}\left(\sqrt{\frac{3}{28}}\right)$
• D. ${\sin }^{-1}\left(\sqrt{\frac{3}{28}}\right)$

Answer 1

The correct option is D ${\sin }^{-1}\left(\sqrt{\frac{3}{28}}\right)$

${\overrightarrow{v}}_v={\overrightarrow{v}}_{bT}+{\overrightarrow{v}}_T$

Diagram

$\tan \varphi =\frac{2\sin {60}^o}{4+2\cos {60}^o}=\frac{\sqrt{3}}{5}$
$\sin \varphi =\sqrt{\frac{3}{28}}$
$\varphi ={\sin }^{-1}\left(\sqrt{\frac{3}{28}}\right)$