Question

A 3.4 kg mess kit sliding on a frictionless surface explodes into two 1.7 kg parts, one moving at 2.7 m/s, due north, and the other at 7.8 m/s, 15° north of east. What is the original speed of the mess kit?

Answer 1

As we know that

Momentum must be conserved.

Magnitude of piece A north = (1.7 kg)(2.7 m/s) = 4.59 kg m/s
Magnitude of piece A east = 0 kg m/s since travelling north.

Magnitude of piece B north = (1.7 kg)(7.8 m/s)sin15 = 3.431940538 kg m/s
Magnitude of piece B east = (1.7 kg)(7.8 m/s)cos15 = 12.80817646 kg m/s

Total momentum north = 8.021940538 kg m/s
Total momentum east = 12.80817646 kg m/s.

Momentum must be conserved, so the total momentum before the explosion must be the same too.

Using Pythagoras's Theorem, overall magnitude
= √[12.80817646² + 8.021940²]
= 15.11293864 kg m/s. Dividing by the mass of the original object (3.4 kg) = 4.444981952 m/s.