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