Question

A satellite in a 100-mile-high circular orbit around Earth has a velocity of approximately 17,500 miles per hour.If this velocity is multiplied by √2 the satellite will have the minimum velocity necessary to escape Earth's gravity and will follow a parabolic path with the center of Earth as the focus.
Required:
Find the distance between the surface of the Earth and the satellite when θ = 50°.

a. Distance between surface of Earth and satellite:4496 miles
b. Distance between surface of Earth and satellite:4322 miles
c. Distance between surface of Earth and satellite:1286 miles
d. Distance between surface of Earth and satellite:643 miles
e. Distance between surface of Earth and satellite:1492 miles

Answer 1

Answer:

64.3 miles ( D)

Step-by-step explanation:

Circular orbit height ( from the center of the earth ) = 100 mile

angle between satellite and earth = 50°

escape velocity = √2 * 17500 =  24748.73 miles /hour

distance between surface of earth and satellite

x = cos ∅

∴ Cos ∅  = x / 100

x = cos 50° * 100   ≈ 64.3 miles