A 21.0 kg body is moving in the direction of the positive x axis with a speed of

Question

A 21.0 kg body is moving in the direction of the positive x axis with a speed of 100.0 m/s when, owing to an internal explosion, it breaks into three parts. One part, whose mass is 7.00 kg, moves away from the point of explosion with a speed of 180 m/s in the direction of the positive y axis. A second fragment, with a mass of 4.00 kg, moves in the direction of the negative x axis with a speed of 250 m/s. What is the velocity of the third fragment? What are the magnitude and direction (in degrees) of this velocity? What is the change in mechanical energy from before to after the explosion?

Explanation / Answer

Explosion is due to internal force so Net external force is zero on system.

hence momentum will not change.

using momentum conservation,

21 * 100 i = 7(180j) + 4(-250i) + (21 - 7 -4)(v)

2100i + 1000i - 1260j = 10v

v = 310i - 126j m/s ..........Ans(A)

b) magnitude = sqrt[310^2 + 126^2] =334.63 m/s

direction= - tan^-1(126/310) = -22.2 deg (below the +ve x axis)

Or 338 deg from +ve x axis in counterclockwise direction.

c) change in ME = 7(180^2)/2 + 4(250^2)/2 + 10(334.6^2)/2 - 21(100^2)/2

= 693185.8 J

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