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 (w$$.r.t. the pieces having equal $$masses) and magnitude of its velocity immediately after the explosion?

Question

Infinity Learn · Accepted Answer

Suppose m be the mass of each piece, flying off perpendicular to one another with same speed u $$(=$$ $$30$$ $$ms-1)$$. Then $$3$$ m is the mass of the third piece. Let V be the velocity of $$3rd$$ piece. According to $$figure.3mv$$ $$cos$$ θ $$=$$ mu, $$3mv$$ $$sin$$ θ $$=$$ mutan θ $$=$$ $$1$$ or θ $$=$$ $$450$$   or $$3v2$$ $$=$$ u $$=$$ $$30$$ $$m/sor$$ v $$=$$ $$102$$ $$ms-1(inclined$$ at $$135$$° w.r.t direction of each $$one)$$

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