If a lighthouse is 144' high, how far out to sea could it's light be seen by a surfer paddling a surfboard?
To determine how far out to sea a surfer paddling a surfboard could see the light of a 144-foot high lighthouse, we need to consider the curvature of the Earth and the height of the surfer's eyes above the water.
1. Firstly, let's assume that the surfer's eyes are about 5 feet above the water's surface. This is an average estimate for a standing surfer.
2. Next, we need to calculate the distance to the horizon based on the height of the surfer's eyes above the water. The formula to calculate the distance to the horizon is √(2Rh), where R is the radius of the Earth (approximately 3,959 miles or 20,902,000 feet) and h is the height of the surfer's eyes above the water. So, the distance to the horizon (Dh) would be Dh = √(2 * 20902000 * 5).
3. Now, we need to factor in the height of the lighthouse. The visible distance of the light from the lighthouse can be calculated as the sum of the distance to the horizon and the height of the lighthouse. Therefore, the total visible distance (Dt) would be Dt = Dh + 144.
By substituting the respective values into the formulas, we can calculate the distance:
Dh = √(2 * 20902000 * 5) ≈ 2092.51 feet.
Dt = 2092.51 + 144 ≈ 2236.51 feet.
Therefore, a surfer paddling a surfboard could potentially see the light of a 144-foot high lighthouse at a distance of approximately 2236.51 feet, or about 0.42 miles, from the shore.