Two persons on ice skates stand face to face and then push each other away (see figure below). Their masses are 50 and 55 kg.

Question

Find the ratio of their speeds immediately afterward.

v50 kg

v55 kg

 = 

Which person has the higher speed? (in kg)?



Answer 1

Let

m1 = 50 kg be the mass of one skater,

v1 (unknown) be his velocity after the push,

m2 = 55 kg be the mass of the other skater,

v2 (unknown) be his velocity after the push.

Before the push their velocities are 0, and therefore their momenta are also 0.

After the push their momenta are m1v1 and m2v2, respectively.

By the law of conservation of momentum, their combined momentum before and after the push must be the same:

m1v1 + m2v2 = 0

By algebraic manipulation

v1/v2 = -m2/m1

Substituting actual numbers

v1/v2 = -55/50 = -1.1

The ratio of their velocities is -1.1.

It is negative because their velocities are in the opposite direction.

You are being asked about the ratio of their speeds, not velocities.

"Speed" being the absolute value of "velocity", the ratio between speeds is 1.1.

And the lighter person ends up with higher speed.