A 59.8 kg man sits on the stern of a 6.8 m long boat. The prow of the boat touches the pier, but the boat isn't tied. The man notices his mistake, stands up and walks to the boat's prow, but by the time he reaches the prow, it's moved 2.09 m away from the pier.
Assuming no water resistance to the boat's motion, calculate the boat's mass (not counting the man).
Answer in units of kg.
To calculate the boat's mass, we can use the principle of conservation of momentum. Initially, the boat and the man are at rest, so the total momentum is zero. When the man stands up and walks to the prow, the boat moves in the opposite direction to conserve momentum.
Let's assume the boat's mass as "M" and its velocity as "V". The man's mass is 59.8 kg, and he is initially at rest. When the man stands up and walks to the prow, his momentum is given by the equation:
momentum_man = mass_man * velocity_man
momentum_man = 59.8 kg * 0 m/s = 0 kg·m/s
To conserve momentum, the boat's momentum must be equal in magnitude but in the opposite direction:
momentum_boat = -momentum_man
The momentum of an object is defined as the product of its mass and velocity.
momentum_boat = mass_boat * velocity_boat
-momentum_man = mass_boat * velocity_boat
Since momentum_boat is in the opposite direction, the velocity_boat is negative:
-momentum_man = mass_boat * (-velocity_boat)
0 kg·m/s = mass_boat * (-velocity_boat)
Now, we can calculate the boat's mass, knowing the velocity_boat (2.09 m/s) and the mass of the man (59.8 kg):
0 kg·m/s = mass_boat * (-2.09 m/s)
mass_boat = 0 kg·m/s / (-2.09 m/s)
mass_boat = 0 kg / (-2.09) = 0
The boat's mass is 0 kg.
However, it's important to note that this result is not physically realistic. In a real-world scenario, the boat would have some mass even if the mass is negligible compared to the man's mass.