Question

A vessel at rest explodes breaking it into three pieces . Two pieces having equal mass fly off perpendicular to one another with the same speed of 30 m/s .The third piece has three times the mass of each other piece . What is the direction and magnitude of its velocity immediately after the explosion

• A. $10\sqrt{2},{135}^0$
• B. $10\sqrt{2},{90}^0$
• C. $10\sqrt{2},{60}^0$
• D. $10\sqrt{2},{30}^0$

Answer 1

The correct option is A $10\sqrt{2},{135}^0$

By momentum conservation

$m_3{v}_3+m_1{v}_1\hat{j}+m_2{v}_2\hat{i}=03m{v}_3=-(m30\hat{i}+m30\hat{j})v_3=-(10\hat{i}+10\hat{j})\left|v_3\right|=10\sqrt{2}\tan \theta \frac{\pi }{2}=angleangle=\frac{\pi }{2}{\tan }^{-1}\frac{10}{10}=180-45=135°$