Christian P. answered • 05/27/23
Accessible STEM tutoring
The way to tackle this problem is through conservation of momentum. Because the problem mentions that the ice is frictionless and doesn't mention anything that might complicate the problem we can assume that all of the momentum is conserved between the skater and the bowling ball.
To solve these problems you should try to write down the momentum before and after the event.
Remember that Momentum (P) is just Mass x Velocity
Before:
This part is simple, we know the mass of the skater and the bowling ball so we can get the total mass.
However the shortcut is that because they are standing still and the velocity is zero the momentum is also zero no matter what the mass is.
Total Mass = skater (70 kg) + bowlingball (7 kg) = 77 kg
Velocity = 0 m/s
Momentum = 77 kg x 0 ms = 0 kg m/s
Now we know that whatever comes after will have to cancel out to zero.
After:
We can find the momentum of the bowling ball because we know everything we need for that.
Mass = 7 kg
Velocity = 20 m/s
Momentum = 140 kg m/s
And because we know the total has to cancel out the momentum of the skater must be -140 kg m/s.
Remember that velocity can be negative if it is going in the opposite direction
Now all we have to do is solve the equation for what's left
Momentum (-140 kg m/s) = mass (70 kg) x velocity (?)
velocity (?) = Momentum (-140 kg m/s) / mass (70 kg) = -2 (m/s)
Therefore our skater is moving at -2 m/s traveling in the opposite direction of the bowling ball. And because the question is only asking for magnitude, we get 2 m/s.
The hardest parts of these kind of questions can sometimes be keeping them organized. Write it out if you can; maybe separate everything before and after the throw onto opposite sides; even using different colors could help.
