Question

A student on the ground observes the sun just as it sets. His friend, who is located 100 meters higher up in a tall building, tells him via cell phone that she observes the sun setting 77 seconds after he does. Assuming that the path of the setting sun is perpendicular to the horizon, use this information to estimate the radius of the Earth.

Answer 1

Rt≅6377Km

Step-by-step explanation:

Take a look at the image. The horizontal line is the horizon, and the angle α corresponds to the earth rotation during the 77 seconds.

With this information, we can know the value of α:

α =
`\alpha= (77s)/(1day)*(1day)/(24H)*(1H)/(60min)*(1min)/(60s)*2*\pi  =0.0056rad`

Since we have formed a rectangle triangle:

`cos\alpha =(Rt)/(Rt+100m)` Solving for Rt:

Rt≅6377467m=6377Km