Answer to Question #250978 in Physics for Pranali

Question

A 37.0 kg body is moving in the direction of the positive x axis with a speed of 325 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 6.3 kg, moves away from the point of explosion with a speed of 366 m/s along the positive y axis. A second fragment, whose mass is 3.6 kg, moves away from the point of explosion with a speed of 424 m/s along the negative x axis. Ignoring the effects of gravity, what is the speed of the third fragment?

Answer 1

The momentum must be conserved along both axes:

$$x: mv=m_2v_2+m_3u\cos\theta,\\ y:0=m_1v_1+m_3u\sin\theta,\\\space\\ \tan\theta=\frac{m_1v_1}{mv-m_2v_2}=\frac{6.3·366}{37·325-3.6(-424)}=0.17,\\\space\\ \theta=9.65°.\\\space\\ u=-m_1v_1/(m_3\sin\theta)=\\ =-m_1v_1/[(m-m_1-m_2)\sin\theta]=\\ =-507.6\text{ kg m/s}.$$