To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.
Let's consider the system consisting of the man, the boat, and the baseball before and after the man throws the ball. The initial momentum of the system is zero because everything is initially at rest. After the man throws the ball, the final momentum of the system should also be zero because the man and the boat are the only objects remaining.
The momentum of an object is given by the product of its mass and velocity (momentum = mass × velocity). We can use this equation to calculate the velocity of the boat after the man throws the ball.
Initial momentum of the system = 0
Final momentum of the system = momentum of the man + momentum of the boat
Let's assign variables: Mass of the man (m₁) = 60 kg Mass of the boat (m₂) = 40 kg Mass of the baseball (m₃) = 0.2 kg Velocity of the baseball (v₃) = 50 m/s Velocity of the boat after the throw (v₂) = ?
Initial momentum of the system: 0 = 0
Final momentum of the system: 0 = (m₁ × 0) + (m₂ × v₂) + (m₃ × 0)
Since the initial and final momentum of the system must be equal, we can solve for v₂:
0 = 0 + (40 kg × v₂) + 0
0 = 40 kg × v₂
Dividing both sides by 40 kg:
0 = v₂
Therefore, the velocity of the boat after the man throws the ball is 0 m/s. The boat does not move because the momentum of the man throwing the ball is canceled out by the equal and opposite momentum of the ball and the boat.