Calculate the time required for a 2,500 kg lifeboat to reach the water if released from a ship
with 9.2-meter freeboard. The lifeboat is leveled with the freeboard. Assume free fall
motion and use g = 9.8 m/s^2
To calculate the time required for the lifeboat to reach the water, we can use the equations of motion for free fall.
The freeboard is the distance between the waterline and the deck of the ship, so when the lifeboat is released from the ship, it will fall this distance.
Given:
Mass of the lifeboat, m = 2,500 kg
Freeboard, h = 9.2 m
Acceleration due to gravity, g = 9.8 m/s^2
We can use the equation: h = (1/2)gt^2, where h is the distance fallen, g is the acceleration due to gravity, and t is the time taken.
Rearranging the equation to solve for t, we have:
2h = gt^2
t^2 = 2h/g
t = √(2h/g)
Substituting the given values, we have:
t = √(2 * 9.2 / 9.8)
t = √(18.4 / 9.8)
t = √1.8775
t ≈ 1.37 seconds
Therefore, it will take approximately 1.37 seconds for the 2,500 kg lifeboat to reach the water if released from a ship with a 9.2-meter freeboard.