Final answer:
Using the conservation of momentum, Mike's velocity is calculated to be 1.375 m/s in the opposite direction of Jenny's movement after they push off each other, with Jenny moving at 5.0 m/s and having a mass of 55 kg while Mike's mass is 200 kg.
Step-by-step explanation:
Jenny and Mike are on ice skates and push off against each other. This scenario exemplifies the conservation of momentum. The conservation of momentum states that the total momentum of a closed system is constant if no external forces are acting on it. In this case, Jenny's mass is 55 kilograms, and when she pushes off Mike, she has a velocity of 5.0 m/s. Mike has a mass of 200 kilograms. To find Mike’s velocity, we use the conservation of momentum formula:
momentum of Jenny = - (momentum of Mike)
(mass of Jenny) × (velocity of Jenny) = - (mass of Mike) × (velocity of Mike)
(55 kg) × (5.0 m/s) = - (200 kg) × (velocity of Mike)
Solving for Mike’s velocity, we get:
(275 kg·m/s) = - (200 kg) × (velocity of Mike)
Mike’s velocity = -(275 kg·m/s) / 200 kg
Mike’s velocity = -1.375 m/s
The negative sign indicates that Mike is moving in the opposite direction to which Jenny is moving. Therefore, Mike's velocity is 1.375 m/s in the direction opposite to Jenny’s. It is assumed that the friction on the ice is negligible.