A 64.1 kg ice skater pushes off his partner and accelerates backwards at 1 m/s2. If the partner accelerates in the opposite direction at 1.6 m/s2 what is the mass of the other skater?Assume that frictional forces are negligible. Express your answer in kg. Your result must contain at least one digit after the decimal point.
Question
A 64.1 kg ice skater pushes off his partner and accelerates backwards at 1 m/s2. If the partner accelerates in the opposite direction at 1.6 m/s2 what is the mass of the other skater?Assume that frictional forces are negligible. Express your answer in kg. Your result must contain at least one digit after the decimal point.
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the push is zero (since they are stationary), and the total momentum after the push should also be zero (since no external force is acting on the system).
The momentum of the first skater after the push is his mass times his velocity, which is 64.1 kg * 1 m/s = 64.1 kg*m/s.
The momentum of the second skater after the push is his mass times his velocity. We don't know his mass (let's call it m), but we know his velocity is 1.6 m/s. So his momentum is m * 1.6 m/s.
Since the total momentum must be zero, the momentum of the first skater must be equal and opposite to the momentum of the second skater. So we can set up the equation:
64.1 kg*m/s = m * 1.6 m/s
Solving for m gives us:
m = 64.1 kg*m/s / 1.6 m/s = 40.0625 kg
So the mass of the second skater is approximately 40.1 kg.
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