Question

The kinetic energy of a body of mass 15 kg is 30 joule. What is its momentum?

Answer 1

This problem is a piece o' cake, IF you know the formulas for both kinetic energy and momentum.  So here they are:

Kinetic energy = (1/2) · (mass) · (speed²)

Momentum = (mass) · (speed)

So, now ... We know that

==> mass = 15 kg,  and

==> kinetic energy = 30 Joules

Take those pieces of info and pluggum into the formula for kinetic energy:

Kinetic energy = (1/2) · (mass) · (speed²)

30 Joules = (1/2) · (15 kg) · (speed²)

60 Joules = (15 kg) · (speed²)

4 m²/s² = speed²

Speed = 2 m/s

THAT's all you need !  Now you can find momentum:

Momentum = (mass) · (speed)

Momentum = (15 kg) · (2 m/s)

Momentum = 30 kg·m/s

(Notice that in this problem, although their units are different, the magnitude of the KE is equal to the magnitude of the momentum.  When I saw this, I wondered whether that's always true.  So I did a little more work, and I found out that it isn't ... it's a coincidence that's true for this problem and some others, but it's usually not true.)