A 48.0-kg body is moving in the direction of the positive x axis with a speed of

Question

A 48.0-kg body is moving in the direction of the positive x axis with a speed of 367 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 6.0 kg, moves away from the point of explosion with a speed of 392 m/s along the positive y axis. A second fragment, whose mass is 3.5 kg, moves away from the point of explosion with a speed of 401 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)
Know: m(3) = 48 - (6 + 3.5) = 38.5 kg

We have in x direction: 48*367 = m(3)x - 3.5*401 => x = 494 m/s

and in y direction: 0 = m(3)y + 6*392 => y = -61.09 m/s

v(3) = sqrt (494^2 + (-61.09)^2 ) = 497.76 m/s

b) All about KINETIC, KE = 1/2 * m * v^2

367^2 * 0.5 * 48 - [ (401^2*0.5*3.5) + (392^2 * 0.5*6) + (498^2 * 0.5 * 38.5) ] = 2.279 * 10^6 J

Hope this helps! ;)

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