# Chapter 9 - Impulse and Momentum - Exercises and Problems: 71

The third piece moves forward with a speed of $1.5\times 10^7~m/s$.

#### Work Step by Step

We can find the mass $m_3$ of the third piece as; $m_1+m_2+m_3 = m_0$ $m_3 = m_0-m_1-m_2$ $m_3 = (2.0\times 10^6~kg)-(5.0\times 10^5~kg)-(8.0\times 10^5~kg)$ $m_3 = 7.0\times 10^5~kg$ We can use conservation of momentum to find the velocity $v_3$ of the third piece after the explosion. $p_f=p_0$ $m_1~v_1+m_2~v_2+m_3~v_3 = m_0~v_0$ $v_3 = \frac{m_0~v_0-m_1~v_1-m_2~v_2}{m_3}$ $v_3 = \frac{(2.0\times 10^6~kg)(5.0\times 10^6~m/s)-(5.0\times 10^5~kg)(-2.0\times 10^6~m/s)-(8.0\times 10^5~kg)(1.0\times 10^6~m/s)}{7.0\times 10^5~kg}$ $v_3 = 1.5\times 10^7~m/s$ The third piece moves forward with a speed of $1.5\times 10^7~m/s$.

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