A 41.0 kg body is moving in the direction of the positive x axis with a speed of

Question

A 41.0 kg body is moving in the direction of the positive x axis with a speed of 292 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 5.5 kg, moves away from the point of explosion with a speed of 497 m/s along the positive y axis. A second fragment, whose mass is 3.0 kg, moves away from the point of explosion with a speed of 417 m/s along the negative x axis.

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

2) How much energy was released in the explosion?

Explanation / Answer

using law of conservationm of momentum

along X-axis

(41*292) = (-3*417) + ((41-5.5-3)*vx)

vx= 406.86 m/s

along y-axis

0 = (5.5*497)+((41-5.5-3)*vy)

vy = -84.1 m/s

magintude is sqrt(vx^2+vy^2) = sqrt(406.86^2+84.1^2) = 415.5 m/s

direction is theta = tan^(-1)(-84.1/406.86) = -11.67 degrees

direction is 11.67 degrees below the X-axis

2) energy released is Kf-ki

Kf = (0.5*5.5*497^2)+(0.5*3*417^2)+(0.5*(41-5.5-3)*415.5^2) = 3745512.125 J

Ki = 0.5*41*292^2 = 1747912 J

energy released is Kf-Ki = 3745512.125 - 1747912= 1.99*10^6 J

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