To find out how long it takes for the equipment to reach the lighthouse top, we can use the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy. Since the velocity is constant, the change in kinetic energy is zero.
Therefore, the work done on the object is equal to the force required to lift it multiplied by the distance it is lifted. We can use the formula:
Work = force x distance
We know that the work done is equal to the power multiplied by the time, so we can use this formula as well:
Work = Power x time
We can use these two formulas to find the time it takes to raise the equipment to the lighthouse top:
force = mg = (14.0 kg)(9.8 m/s^2) = 137.2 N
distance = 106 m
Work = force x distance = 137.2 N x 106 m = 14,532.8 J
Power = 3.00 x 10^2 W
We can now substitute these values into the second formula:
Work = Power x time
14,532.8 J = 3.00 x 10^2 W x time
time = Work / Power = (14,532.8 J) / (3.00 x 10^2 W) = 484.4 seconds
So, it takes the equipment approximately 484.4 seconds (8 minutes and 4.4 seconds) to reach the lighthouse top.
I hope this helps :)