Suppose that you and a friend are on a sailboat near the equator, watching the S

Question

Suppose that you and a friend are on a sailboat near the equator, watching the Sun set over calm water. You are reclining on the main deck of the boat at sea level, and your friend is standing on a raised deck a distance H = 1.65 m above the surface of the water. You start a stopwatch just as the top of the Sun disappears from your vantage, and you stop the watch when your friend tells you that the sun has disappeared from his/her vantage point. You find that t = 11.7 s has elapsed between these two events.

(a) Through what angle (measured in radians) has the earth turned during the t = 11.7 s interval?
________ rad

(b) What is the approximate radius R of Earth?
_________ m

Explanation / Answer

Here,

a) time interval , t = 11.7 s

theta = angular speed * time

theta = (2pi/(24 * 3600)) * 11.7 rad

theta = 8.506 *10^-4 radian

the angle that earth rotated is 8.506 *10^-4 radian

b) for the earth motion ,

change in height = R * sin(theta)

1.65 = R * sin(8.506 *10^-4)

R = 1939.8 m

the radius of earth using this calculation is 1939.8 m

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