A 100 kg mass, initially at rest, is blown apart into a 60 kg piece and a 40 kg piece. After the blast, the two masses are moving apart with a relative velocity of 60 m/s. The speed of the 60 kg mass is
A) 88 m/s.
B) 67 m/s.
C) 51 m/s.
D) 40 m/s.
E) 24 m/s.

Question

Quizplus · Accepted Answer

The law of conservation of momentum states that the total momentum of a closed system is constant if no external forces are acting on it. Initially, the momentum of the system is zero because the mass is at rest. After the explosion, the momentum of the two pieces must still sum to zero because the system is closed and no external forces are acting on it. Let $v_{60}$ be the velocity of the 60 kg mass and $v_{40}$ be the velocity of the 40 kg mass. The relative velocity between the two masses is given as 60 m/s. We can express the conservation of momentum as:$$60kg \cdot v_{60} + 40kg \cdot v_{40} = 0$$And we know the relative velocity is:$$v_{40} - v_{60} = 60 m/s$$Solving these equations, we find that $v_{60} = 24 m/s$ and $v_{40} = 84 m/s$, with the direction of $v_{40}$ being opposite to $v_{60}$ to satisfy the conservation of momentum. Hence, the speed of the 60 kg mass is 24 m/s.

A 100 Kg Mass, Initially at Rest, Is Blown Apart