Question

A rocket is launched straight up from Earth's surface at a speed of 15,000 m/s. What is its speed when it is very far away from the earth

Answer 1

1/2 m v2^2 = 1/2 m v1^2 - G M m / R conservation of energy

v1^2 - v2^2 = 2 G M / R rearranging terms

2 G M / R = 2 * 6.67 * 5.98 / 6.37 E7 = 1.25E8

v1^2 - v2^2 = 1.25E8

v2^2 = v1^2 - 1.25E8 = (1.5^2 - 1.25) * E8

v2 = 1.00E4 = 10,000 m/s