A boy sitting in a boat at rest throws a 6.4kg object horizontally out of the boat at 10.0 m/s. The mass of the boy is 26kg and the mass of the boat is 45kg. Calculate the velocity of the boat just after the package is thrown. I used momentum before = momentum after. 6.4kg*10.0m/s devided by 71kg = .9 m/s. Is this correct?
I didn't punch the calculator, but the setup is correct.
Thanks
Yes, your calculation is correct. To understand how you arrived at the answer using the principle of momentum conservation, let's go through the steps:
1. Identify the relevant masses and velocities:
- The mass of the object thrown is 6.4 kg.
- The velocity of the object thrown is 10.0 m/s.
- The mass of the boy is 26 kg.
- The mass of the boat is 45 kg.
2. Apply the principle of momentum conservation:
According to the principle of momentum conservation, the total momentum before an event should be equal to the total momentum after that event.
Momentum before = Momentum after
The momentum before the object is thrown can be calculated as the sum of the momentum of the boy and the momentum of the boat:
Momentum before = (mass of the boy * velocity of the boy) + (mass of the boat * velocity of the boat)
The momentum after the object is thrown can be calculated as the sum of the momentum of the boy (since he is not affected by the throw) and the momentum of the boat (which changes due to the throw):
Momentum after = (mass of the boy * velocity of the boy) + (mass of the boat * velocity of the boat')
3. Plug in the values:
- mass of the object thrown = 6.4 kg
- velocity of the object thrown = 10.0 m/s
- mass of the boy = 26 kg
- mass of the boat = 45 kg
4. Calculate the velocity of the boat just after the object is thrown:
Rearrange the equation using the principle of momentum conservation:
(mass of the boy * velocity of the boy) + (mass of the boat * velocity of the boat) = (mass of the boy * velocity of the boy) + (mass of the boat * velocity of the boat')
Rearranging for the velocity of the boat':
velocity of the boat' = [(mass of the boy * velocity of the boy) + (mass of the boat * velocity of the boat) - (mass of the boy * velocity of the boy)] / mass of the boat
velocity of the boat' = [(26 kg * 0 m/s) + (45 kg * 0 m/s) - (26 kg * 10 m/s)] / 45 kg
velocity of the boat' = (-260 kg*m/s) / 45 kg
velocity of the boat' = -5.78 m/s (Note: The negative sign indicates that the boat is moving in the opposite direction to the thrown object)
5. Calculate the magnitude of the velocity:
To find the magnitude of the velocity, ignore the negative sign:
magnitude of the velocity of the boat' = |-5.78 m/s| = 5.78 m/s
So, the calculated velocity of the boat just after the package is thrown is 5.78 m/s.