A bowling ball is floating motionless in a vacuum just minding its own business. Suddenly it explodes into two pieces. The instant after the explosion, one piece has a mass of 450.0 g and flies off to the right at 0.58 m/s. The remaining piece flies off to the left at 0.98 m/s..
Using this information, figure out what the mass of the bowling ball was before the explosion. Note that the motion remains in one dimension the whole time!

Question

A bowling ball is floating motionless in a vacuum just minding its own business. Suddenly it explodes into two pieces. The instant after the explosion, one piece has a mass of 450.0 g and flies off to the right at 0.58 m/s. The remaining piece flies off to the left at 0.98 m/s..
Using this information, figure out what the mass of the bowling ball was before the explosion. Note that the motion remains in one dimension the whole time!

matt101 · Answer

You can solve this using conservation of momentum. The initial momentum is 0 kg m/s since the bowling ball is stationary. If the ball split into two pieces, the momentum of one piece will be equal (but opposite) to the momentum of the other:

$$m_1v_1=-m_2v_2$$
The question gives us values for 3 of the 4 variables in that equation, so we can solve for the fourth. No need to convert g to kg here (you'd just end up dividing both sides by 1000, keeping them equal).

$$(450)(0.58)=-m_2(-0.98)$$$$m_2=266$$
Notice the velocity on the right side is negative, because that piece is moving in the opposite direction. The negative velocity cancels the negative momentum. The mass of the second fragment is 266 g, so the mass of the original bowling ball is the sum of the two fragments: 450+266=716 g.

Does that make sense?