Jack has a mass of 50 kg and Jill has a mass of 40 kg. After they push off from each from each other, Jill is moving to the right at 5 m/s. If they both are on the center of an ice rink and push off from each other, determine Jack's speed?

4 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision.

But,

Total momentum before collision = 0 m/s (Both are at the center of the ice rink before the push).

0 = mv+m'v'

Where m = mass of Jack, m' = mass of Jill, v = final speed of Jack, v' = final speed of Jill

-mv = m'v' ... Equation 1

make v the subject of the equation

v = m'v'/-m ... Equation 2

Given: m = 50 kg, m' = 40 kg, v' = 5 m/s.

Substitute into equation 2

v = - 40 (5) / 50

v = - 200/50

v = - 4 m/s

Note: The negative sign shows that Jack moves to the left with a speed of 4 m/s

Hence Jack's speed = 4 m/s