Problem 1 What is the minimum velocity of a projectile not

Problem 1. What is the minimum velocity of a projectile ( not a rocket) fired vertically from the Earth so that it escapes from the Earth’s gravitational pull? This is known as its escape velocity. You can neglect air-resistance. HInt: If the velocity of the projectile falls to zero it will be pulled back to Earth

Solution

The radius of the Earth, R_E, is about 6371 km and g = 0.0098 km/s². The escape velocity or speed away from the Earth\'s surface is:

s_e = (2gR_E)

s_e = [2*(0.0098 km/s²)*(6371 km)]

s_e = (124.872 km²/s²)

s_e = 11.175 km/s

Thus, the escape velocity from the surface of the Earth is about 11.2 km/s or 25,055 miles per hour.

This is the same value calculated from s_e = (2GM_E/R_E) at the Earth\'s surface.