Physics Problem: Conservation of Momentum
What is the speed at which the catcher slides on the ice?
A 149 kg baseball moving at 17.7 m/s is caught by a 57 kg catcher at rest on an ice skating rink, wearing frictionless skates. With what speed does the catcher slide on the ice?
Answer:
The speed at which the catcher slides on the ice is 12.8 m/s.
When a 149 kg baseball moving at 17.7 m/s is caught by a 57 kg catcher at rest on an ice skating rink, the conservation of momentum principle can be applied to find the speed at which the catcher slides on the ice.
By applying the law of conservation of energy, the equation becomes:
MaVa + MbVb = (Ma+b)(Va+b)
Where:
- Ma = mass of baseball = 149 kg
- Mb = mass of catcher = 57 kg
- Va = initial speed of baseball = 17.7 m/s
- Vb = initial speed of catcher = 0 m/s
- v = final speed of both baseball and catcher
By substituting the values into the equation, we get:
(149 kg)(17.7 m/s) + (57 kg)(0 m/s) = (149 kg + 57 kg)(v)
v = (2637.3 kgm/s) / (206 kg)
Therefore, the speed at which the catcher slides on the ice is 12.8 m/s.