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

Moderate

Solution

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.
$3 mv \cos θ = mu, 3 mv \sin θ = mu$
$\tan θ = 1 or θ = 45^{0} or \frac{3 v}{\sqrt{2}} = u = 30 m / s$
or $v = 10 \sqrt{2} {ms}^{- 1}$
(inclined at 135° w.r.t direction of each one)

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