Question

A 50.0 kg body is moving in the direction of the positive x axis with a speed of 384 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 9.0 kg, moves away from the point of explosion with a speed of 353 m/s along the positive y axis. A second fragment, whose mass is 5.0 kg, moves away from the point of explosion with a speed of 313 m/s along the negative x axis.

What is the speed of the third fragment? Ignore effects due to gravity.

How much energy was released in the explosion?

Answer 1

mass of third fragment will be

m3 = 50 - 9 - 5 = 36 kg

now, use conservation of momentum in x direction

5 * - 313 + 36 * v3 = 50 * 384

v3 ( x - component) = 576.8 m/s

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use conservation of momentum in y direction

9 * 353 + 5 * 0 + 36 * v3 = 0

v3 = - 88.25 m/s ( y - component)

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energy released

final - initial

E = (1/2 * 9 * 353² + 1/2 * 5 * 313² + 1/2 * 36 * 576.8² + 1/2 * 36 * 88.25²)  - (1/2 * 50 * 384²)

E = 3.248e6 J