You find yourself stuck on top of the ice in the middle of a frozen pond. Your friend John, a professional curler, is standing on the shoreline. Trying to help you get to the other side of the lake, John pulls out his trusty 18 kg curling stone slides it to you at 3 m/s. You carefully trap it, and then push it back towards John at 2 m/s. (A) If your mass (s 60 kg, what is your velocity after you slide the stone back towards John?(B) What was the impulse on you? The stone?
Can you explain with details?

Firstly, when John pushed the ball towards you, the ball had a momentum (momentum is only possessed by a body in motion). The momentum is the product of a body's velocity and its mass.

The ball's initial momentum towards John = mass x initial velocity

ball's initial momentum = (18 kg) x (3 m/s) = 54 kg-m/s

You initially had a momentum of zero. This is because you were just standing on the other side.

your initial momentum = mass x initial velocity

your initial momentum = (60 kg) x (0 m/s) = 0 kg-m/s

When the ball got to you, it impacted some of its momentum to you in accordance with the laws of conservation of momentum. In the process, the momentum of the curling ball reduces and the velocity with which it travels back to John is reduces. You on the other hand will now have a momentum from pushing the ball towards John, and your final velocity is no longer zero.

Final momentum of the ball = mass x final velocity = (18 kg) x (2 m/s) = 36 kg-m/s

Your final momentum = mass x final velocity = (60 kg) x v = 60v

According to the conservation of momentum, the total initial momentum in the system (the relationship between you and the curling ball) must be equal to the final momentum of the system. This means that the total initial momentum of the system, must be equal to the total final momentum of the system.

Total initial momentum of the system = the curling ball's initial momentum plus your initial momentum.

==> 54 kg-m/s + 0 kg-m/s = 54 kg-m/s

This value must be equal to the final momentum of the system.

The total final momentum of the system = the curling ball's final momentum + your final momentum

==> 36 kg-m/s + 60v = 54 ------obeying conservation of momentum law

36 + 60v = 54

60v = 54 - 36 = 18

v = 18/60 = 0.3 m/s ---------This is your final velocity

B) The impulse is the change in the momentum of a body

your final velocity = mass x final velocity = 60 kg x 0.3 m/s = 18 kg-m/s

for you, your impulse = your final momentum minus your initial momentum

your impulse = 18 kg-m/s - 0 kg-m/s = 18 kg-m/s

For the ball, impulse = ball's final momentum minus ball's initial momentum

ball's impulse = 36 kg-m/s - 54 kg-m/s = -18 kg-m/s

You gained the momentum that was lost from the curling ball