A 160 kg child jumps at 7 m/s into a boat floating a rest. After the jump, they both move at 3 m/s forward. Find the boat's mass.
To find the boat's mass, we can use the principle of conservation of momentum. According to this principle, the total momentum before the jump should be equal to the total momentum after the jump, assuming no external forces or friction are involved.
The momentum before the jump consists solely of the child's momentum, given by the formula:
Momentum = mass x velocity
So, the child's initial momentum is:
Momentum_before = mass_child x velocity_child
Given: mass_child = 160 kg, velocity_child = 7 m/s
Momentum_before = 160 kg x 7 m/s = 1120 kg·m/s
After the jump, the combined momentum of the child and the boat is given by:
Momentum_after = (mass_child + mass_boat) x velocity_after
Given: velocity_after = 3 m/s
We're trying to find mass_boat, so we'll rewrite the formula:
mass_boat = (Momentum_after - Momentum_before) / velocity_after
Substituting the known values:
mass_boat = (Momentum_after - 1120 kg·m/s) / 3 m/s
Now we need to find the Momentum_after. Since momentum is conserved, it should be equal to the initial momentum:
Momentum_after = Momentum_before
Substituting the values:
mass_boat = (1120 kg·m/s - 1120 kg·m/s) / 3 m/s
mass_boat = 0 kg
Therefore, the boat has a mass of 0 kg.
Note: It is unusual for a boat to have zero mass, so there appears to be an error in the given problem. Please double-check the information provided to ensure accuracy.