Determine its escape velocity in miles/s?

[Math10]

Homework Statement

A space probe is to be launched from a space station 200 miles above Earth. Determine its escape velocity in miles/s. Take Earth's radius to be 3960 miles.

Homework Equations

None.

The Attempt at a Solution

m(dv/dt)=-(mgR^2)/(x+R)^2
dv/dt=-(gR^2)/(x+R)^2
Now what?
The answer is 6.76 miles/s.

 

[Andrew Mason]

The Attempt at a Solution

m(dv/dt)=-(mgR^2)/(x+R)^2
dv/dt=-(gR^2)/(x+R)^2
Now what?

What is the condition for escape? (hint: what is the potential energy and what is the kinetic energy of the body when it has reached a distance where the Earth's gravity is negligible and the body is just barely moving?). Use the principle of conservation of total energy to determine what its speed must be initially in order to achieve that distance.

Suggestion: I would convert to metric, do the calculations and convert back.

AM