A 90 kg fisherman at one end of a 3 m long 150 kg rowboat walks to the other end. To someone standing on the shore, what distance does the rowboat move relative to its initial position
To determine the distance the rowboat moves relative to its initial position, we need to consider the concept of center of mass. The center of mass is the point where the mass of an object can be considered to be concentrated and behaves as if the entire mass was located there.
Initially, the 90 kg fisherman is situated at one end of the rowboat, while the 150 kg rowboat is stationary. The system's center of mass is located closer to the fisherman since he has a smaller mass compared to the rowboat.
When the fisherman walks to the other end of the rowboat, his mass shifts the center of mass towards that end. As a result, the rowboat moves in the opposite direction to maintain the system's overall center of mass.
To calculate the distance the rowboat moves, we need to utilize the principle of conservation of momentum. The initial momentum of the system, which is initially at rest, is zero. After the fisherman moves to the other end of the rowboat, the system gains momentum in the opposite direction to maintain zero momentum. This means the rowboat will move an equal distance but in the opposite direction to the fisherman's displacement.
To find the distance the rowboat moves, we can identify the ratios of the masses and distances involved.
The fisherman has a mass of 90 kg, while the rowboat has a mass of 150 kg. Since the mass of the rowboat is greater than that of the fisherman, the rowboat will move a smaller distance compared to the fisherman's displacement.
To determine the precise distance, we can use the ratio of masses:
Mass ratio = mass of fisherman / mass of rowboat
Mass ratio = 90 kg / 150 kg
Mass ratio = 0.6
Since the fisherman moves a distance of 3 m, we can calculate the distance the rowboat moves using the mass ratio:
Distance rowboat moves = Mass ratio * Distance fisherman moves
Distance rowboat moves = 0.6 * 3 m
Distance rowboat moves = 1.8 m
Therefore, the rowboat moves a distance of 1.8 meters relative to its initial position, as observed by someone standing on the shore.