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The straightest road in the USA is the Simi Highway, Route 28, in Michigan. A driver, seated in a car, is viewing a deer crossing the road. The eyes of the driver are about 3 ft above the ground, and the deer is about 3 ft in height. If the radius of the Earth is 6400 km.

Required:
a. How far away can the driver see the very top of the deer as it emerges from below the horizon?
b. If the deer is 5 feet long, what angle does the deer subtend from the driver (i.e. what is the angular size of the 5’ long deer at this distance)?

Sagot :

Answer:

a) d = 3.6 km

b) 0.024°

Explanation:

To see the top of a 1 m tall deer over the surface of a 6400 km radius perfect sphere, the angle subtended is

cosθ = 6 400 000 / (6 400 001)

θ = 0.0320293...°

d = Rtanθ = 6 400 000tan0.0320293

d = 3,577.708... m

5 ft = 1.524 m

tanθ = 1.524 / 3577.7

θ = 0.0244063...°

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