A 24.0-kg body is moving in the direction of the positive x axis with a speed of

Question

A 24.0-kg  body is moving in the direction of the positive x axis with a speed of 325 kg when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 7.0 kg, moves away from the point of explosion with a speed of 468 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 421 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?

Explanation / Answer

a) as M = m1+ m2 + m3

mass m3 = 24 - (7+ 5) = 12 kg

We have in x direction: 24*325 = m3 x - 5 * 421

=> x = 283.75 m/s

and in y direction: 0 = m3*y + 7*468 => y = -273 m/s

v(3) = sqrt (283.75^2 + (-273)^2 ) = 393.75 m/s

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b) KE = 1/2 * m * v^2

so 0.5 * 24* 325^2 -(0.5* 7 * 468^2) -(0.5*5 * 421^2) -(0.5 * 12 * 393.75^2)

total KE = 8.72 *10^5 Joules

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