A child in a boat throws a 5.90-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 26.6 kg and the mass of the boat is 38.2 kg . Calculate the velocity of the boat immediately after, assuming it was initially at rest.
conserving momentum,
(38.2+26.6)v = -5.90*10
To calculate the velocity of the boat immediately after the child throws the package, we can use the law of conservation of momentum. This law states that the total momentum of a system before an event is equal to the total momentum after the event, assuming no external forces act on the system.
The momentum of an object is calculated by multiplying its mass by its velocity. So, we can start by calculating the momentum of the package before it is thrown:
Momentum of the package before = mass of the package × velocity of the package before
Since the child throws the package horizontally and its speed is given as 10.0 m/s, the horizontal velocity of the package before is also 10.0 m/s. Thus:
Momentum of the package before = 5.90 kg × 10.0 m/s
Next, we need to calculate the momentum of the child and the boat immediately after the package is thrown. Assuming the boat was initially at rest, the momentum of the child and the boat after the event is given by:
Momentum of the child and boat after = (mass of the child + mass of the boat) × velocity of the boat after
Since we need to find the velocity of the boat after the event, we can rearrange the equation to solve for it:
Velocity of the boat after = (Momentum of the child and boat after) / (mass of the child + mass of the boat)
Substituting the given values:
Velocity of the boat after = (Momentum of the package before) / (mass of the child + mass of the boat)
= (5.90 kg × 10.0 m/s) / (26.6 kg + 38.2 kg)
Calculating this expression gives us the velocity of the boat immediately after the child throws the package.