To find the total momentum of the system after the puck is caught by the goalkeeper, we can use the principle of conservation of momentum. Initially, the momentum of the puck (Puck) can be calculated using the formula:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
For the puck:
\[ \text{Momentum}{\text{puck}} = m{\text{puck}} \times v_{\text{puck}} = 0.16 , \text{kg} \times 40 , \text{m/s} = 6.4 , \text{kg m/s} \]
The goalkeeper is at rest, so their initial momentum is:
\[ \text{Momentum}{\text{goalkeeper}} = m{\text{goalkeeper}} \times v_{\text{goalkeeper}} = 120 , \text{kg} \times 0 , \text{m/s} = 0 , \text{kg m/s} \]
The total initial momentum of the system before the collision is:
\[ \text{Total Momentum}{\text{initial}} = \text{Momentum}{\text{puck}} + \text{Momentum}_{\text{goalkeeper}} = 6.4 , \text{kg m/s} + 0 , \text{kg m/s} = 6.4 , \text{kg m/s} \]
After the puck is caught, the puck and goalkeeper move together as one mass, so we can find their combined velocity using the total momentum.
Let \(v_f\) be the final velocity of the combined system:
\[ \text{Total Momentum}{\text{final}} = (m{\text{puck}} + m_{\text{goalkeeper}}) \times v_f \]
Equating the initial and final momentum:
\[ 6.4 , \text{kg m/s} = (0.16 , \text{kg} + 120 , \text{kg}) \times v_f \]
\[ 6.4 , \text{kg m/s} = 120.16 , \text{kg} \times v_f \]
Now, solving for \(v_f\):
\[ v_f = \frac{6.4 , \text{kg m/s}}{120.16 , \text{kg}} \approx 0.0532 , \text{m/s} \]
Total momentum after the puck is caught: \[ \text{Total Momentum}{\text{final}} = (m{\text{puck}} + m_{\text{goalkeeper}}) \times v_f = 6.4 , \text{kg m/s} \]
Now, to identify the object with greater momentum after the puck is caught:
After the puck is caught, the total momentum of the system (puck + goalkeeper) is still 6.4 kg m/s, which is the momentum of both combined. The goalkeeper, initially at rest, has a momentum of 0 kg m/s before the puck is caught and gains momentum through the collision. However, the individual momentum of the goalkeeper alone after catching the puck (which is now included in the total) cannot be distinguished because they now move together as one entity. Therefore, we conclude that before the catch, the puck had the greater momentum, while after the catch, the total momentum remains constant at 6.4 kg m/s, indicating the system's momentum rather than individual contributions.
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