Q. Escape Velocity

An object will conquer the force of gravity when its kinetic energy in the direction away from earth exceeds its potential energy. We find the smallest kinetic energy required by solving K.E. = P.E..

Then

mv²/2=mgr,

Where m is the mass of object and v is its velocity and g is the acceleration due to gravity and r is the radius of the earth.

Solving for v

v²= 2gr

v =√2gr

Taking the earth's radius as 3960 miles as well as the acceleration due to gravity as 32 feet per second² we have

V=√232/5280 × 3960

Which reduces to 6.9 miles per second