A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of
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Momentum of one piece \(= \frac{M}{4} \times 3\)
Momentum of the other piece \(= \frac{M}{4} \times 4\)
∴ ∴ Resultant momentum \(= \sqrt{\frac{9M^{2}}{16} + M^{2}} = \frac{5M}{4}\)
The third piece should also have the same momentum. Let its velocity be v, then
\(\frac{5M}{4} = \frac{M}{2} \times v\) or \(v = \frac{5}{2} = 2.5 \, m / sec\)
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