Your answer is partially correct. Try again. A 26 kg body is moving through spac

Question

Your answer is partially correct. Try again. A 26 kg body is moving through space in the positive direction of an x axis with a speed of 120 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 5.2 kg, moves away from the point of explosion with a speed of 90 m/s in the positive y direction. A second part, with a mass of 8.2 kg, moves in the negative x direction with a speed of 610 m/s. What are the (a)x-component and (b) y om p o n e n t of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force.

Explanation / Answer

The mass of the third part is 26 - 5.2 - 8.2 = 12.6 kg

The x copmonent of the velocity is found conserving x momentum

(26)(120) = (8.2)(-610) + (12.6)(v)

v = 644.6 m/s in the positive x direction

The y component is

0 = (5.2)(90) + (12.6)(v)

v = -37.1 m/s

The net velocity is sqrt[(37.1^2) + (644.6)^2] = 645.7 m/s

The initial enegry is .5(26)(120^2) = 187200 J

The final energy = .5(5.2)(90)^2 + (.5)(8.2)(610^2) + (.5)(12.6)(645.7^2) = 4173319 J

The energy difference is 4173319 - 187200 = 3986119 J

So, 3986119 J (3.99 X 10^6 J) of energy was released

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