Question

You are lying on a beach, your eyes 20cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds until the Sun fully disappears again, you can estimate the Earth’s radius. But for this Problem, use the known radius of the Earth to calculate the time t

Answer 1

Let us say that by the time t, Earth rotates by an angle , We know the radius of the earth is 6378 km. We know that the height of the person changes from 20 cm to 150 cm, hence we write the angle as,

Substituting we get,

Earth takes about 4 mins for 1 degree movement hence for 0.035 degrees, the time taken is,

Answer 2

Let us say that by the time t, Earth rotates by an angle , We know the radius of the earth is 6378 km. We know that the height of the person changes from 20 cm to 150 cm, hence we write the angle as,

Substituting we get,

Earth takes about 4 mins for 1 degree movement hence for 0.035 degrees, the time taken is,