A body falls from infinity and reaches the surface of the Earth.

Given:

• Earth radius = 6400 km
• g = 9.8 m/s²

Find the velocity on reaching Earth's surface.

The velocity acquired by a body falling from infinity is called the escape velocity.

Using:

v = √(2gR)

Convert radius:

R = 6400 × 10³ m

Substituting:

v = √(2 × 9.8 × 6400 × 10³)

v ≈ 11200 m/s

= 11.2 km/s

Final Answer

11.2 km/s