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

1 answer

To calculate the time required for the lifeboat to reach the water, we can use the following equation of motion for free fall:

h = (1/2)gt^2

Where:
h = vertical distance traveled (freeboard + height of the lifeboat)
g = acceleration due to gravity (9.8 m/s^2)
t = time

Given:
freeboard (h) = 9.2 meters
mass of the lifeboat (m) = 2,500 kg
g = 9.8 m/s^2

The total height (h) traveled by the lifeboat is the sum of the freeboard and the height of the lifeboat:
h = 9.2 m + height of the lifeboat

We need to determine the height of the lifeboat to calculate the total height (h).

Since the lifeboat is leveled with the freeboard, the height of the lifeboat is equal to the freeboard:
height of the lifeboat = 9.2 m

Substituting the values into the equation of motion:

9.2 m + 9.2 m = (1/2)(9.8 m/s^2)t^2

Simplifying the equation:

18.4 m = 4.9 m/s^2 * t^2

Dividing both sides of the equation by 4.9 m/s^2:

3.755 t^2 = 18.4 m / 4.9 m/s^2

3.755 t^2 = 3.755

Dividing both sides of the equation by 3.755:

t^2 = 1

Taking the square root of both sides of the equation:

t = √1

t = 1 second

Therefore, the time required for the 2,500 kg lifeboat to reach the water is 1 second when released from a ship with a 9.2-meter freeboard, assuming free fall motion and using g = 9.8 m/s^2.