Question

A spaceship of speed $v_0$ travelling along +y axis suddenly shots out one fourth of its part with speed $2v_0$ along + x – axis. x,y axes are fixed with respect to ground. The velocity of the remaining part is:

• A. $\frac{\sqrt{13}}{3}{v}_0$
• B. $\frac{\sqrt{5}}{3}{v}_0$
• C. $\frac{\sqrt{20}}{3}{v}_0$
• D. $\frac{2}{3}{v}_0$

Answer 1

The correct option is C

$\frac{\sqrt{20}}{3}{v}_0$

$m{v}_0\hat{j}=\frac{m}{4}\times 2v_0\hat{i}+\frac{3m}{4}\overrightarrow{v}$

$\Rightarrow \frac{3m}{4}\overrightarrow{V}=m{v}_0\hat{j}-\frac{m{V}_0}{2}\hat{i}$

$\Rightarrow |\overrightarrow{V}|=\frac{\sqrt{20}}{3}{v}_0$