A rocket traveling through the atmosphere experiences a linear air resistance −kv. Find th...

A rocket traveling through the atmosphere experiences a linear air resistance −kv. Find the differential equation of motion when all other external forces are negligible. Integrate the equation and show that if the rocket starts from rest, the final speed is given by

where V is the relative speed of the exhaust fuel, , m0 is the initial mass of the rocket plus fuel, and m is the final mass of the rocket.