Question

A 32.0-$kg$ body is moving in the direction of the positive x axis with a speed of 376 $m/s$ when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 9.5 $kg$, moves away from the point of explosion with a speed of 371 $m/s$ 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 486 $m/s$ 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?

Answer 1

1) Using unit vectors,
initial p = mv = 32.0kg * 376m/s = 12032 i kg·m/s
final p = 9.5kg*371m/s j - 3.0kg * 486m/s i + (32.0-9.5-3.0)kg * v

Momentum is conserved (no EXTERNAL forces), so
12032 i kg·m/s = -1458`kg·m/s i + 3524.5kg·m/s j + 19.5kg * v
19.5kg * v = [13490 i - 3524.5 j] kg·m/s
v = [691.794 i - 180.743 j] m/s

speed = |v| = √(691.794² + 180.743²) m/s = 667.765 m/s

2) initial KE = ½ * 32.0kg * (376m/s)² = 3.262*10^6 J
final KE = ½(9.5*371² + 3.0*486² + 19.5*667.765²) = 5.355*10^6 J
meaning the explosion released= 5.355 MJ