Question

A proposed space elevator would consist of a cable stretching from the earth's surface to a satellite, orbiting far in space, that would keep the cable taut. A motorized climber could slowly carry rockets to the top, where they could be launched away from the earth using much less energy.
What would be the escape speed for a craft launched from a space elevator at a height of 56,000 km?

Answer 1

Answer:

The escape speed for the craft is 1.49 m/s.

Explanation:

In this case we need to find the escape speed for a craft launched from a space elevator at a height of 56,000 km. The escape velocity is given by :

$v=\sqrt{\dfrac{2GM}{d}}$

Here,

G is universal gravitational constant

M is mass of earth

d = r + h, r is radius of Earth

$v=\sqrt{\dfrac{2\times 6.67\times 10^{-11}\times 5.972 \times 10^{24}}{(6,371 \times 10^3\times 56000\times 10^3)}}\\\\v=1.49\ m/s$

So, the escape speed for the craft is 1.49 m/s.