a boat of mass 90 kg is floating in still water a body of mass 30 kg walks from the stern to the boat the length of the boat is 3m. calculate the distance through which the boat move.
He doesn't move actually 3 meters, as the boat is moving a distance d beneath him. So his mass actually moves (3-d).
The center of mass should remain at zero.
30(3-d)+90*d=120*0
solve for d. Negative means in the direction opposite to his movement.
To calculate the distance through which the boat moves when the body of mass 30 kg walks from the stern to the boat, we need to use the principle of conservation of momentum.
The initial momentum of the boat and the person is zero since they are both stationary. When the person walks to the boat, the combined system of the person and the boat will have a final momentum. According to the law of conservation of momentum, the total momentum before and after the interaction should be the same.
Let's denote the distance through which the boat moves as "d", and assume that the boat starts moving in the opposite direction to the person's movement.
The initial momentum of the boat can be calculated as the product of its mass (90 kg) and initial velocity (0 m/s), which gives us 0 kg m/s. The initial momentum of the person is also zero.
The final momentum of the combined system can be calculated as the sum of the momentum of the boat and the person. The momentum of the boat can be calculated as the product of its mass (90 kg) and final velocity (v_b). The momentum of the person can be calculated as the product of their mass (30 kg) and final velocity (v_p). Since the boat and the person move in opposite directions, their velocities will have opposite signs.
So, the equation for conservation of momentum can be written as:
(90 kg)(0 m/s) + (30 kg)(-v_p) = (90 kg)(v_b) + (30 kg)(v_p)
Simplifying the equation:
-30v_p = 90v_b - 30v_p
Collecting like terms:
60v_p = 90v_b
Dividing by 30:
2v_p = 3v_b
We also know that the person moves a distance of 3 m on the boat while the boat moves a distance of "d" in the opposite direction. Therefore, we can set up the equation:
2v_p = 3v_b
Rearranging the equation, we get:
v_b = (2/3)v_p
Substituting the value of v_b into the expression for the distance traveled by the boat:
d = (2/3)v_p * t
where t is the time it takes for the person to move the distance of 3 m on the boat.
Therefore, to calculate the distance through which the boat moves, we need to know the time it takes for the person to move the distance of 3 m on the boat. Without that information, we cannot provide a specific numerical answer.