A rocket explodes into three pieces of equal mass.Immediately after the explosion their velocities are (120 m/s,south),(240 m/s,north)and (120 m/s east).What was the velocity of the rocket's center of mass before the explosion?
A)40 m/s,northeast
B)57 m/s,northeast
C)120 m/s,northeast
D)170 m/s,northeast

Question

Quizplus · Accepted Answer

First, we need to find the total momentum before the explosion, which is zero since the rocket was at rest. After the explosion, momentum is still conserved. We can use vector addition to find the velocity of the center of mass, which is the weighted average of the three pieces of the rocket based on their masses:

Total mass = 3m (since the rocket was divided into 3 equal pieces)
Velocity of the center of mass = [m(120 m/s, south) + m(240 m/s, north) + m(120 m/s, east)] / 3m
= (120/3, -120/3) + (240/3, 0) + (0, 120/3)
= (120, 0)

Therefore, the velocity of the rocket's center of mass before the explosion was 120 m/s to the right (east) and 0 m/s up/down (north/south), which gives a velocity vector of 120 m/s, northeast. The closest answer option is B.

A Rocket Explodes into Three Pieces of Equal Mass