The weight of a particle varies with altitude such that is the radius of the earth and...

The weight of a particle varies with altitude such that is the radius of the earth and r is the distance from the particle to the earth's center. If the particle is fired vertically with a velocity from the earth's surface, determine its velocity as a function of position r What is the smallest velocity required to escape the earth's gravitational field, what is and what is the time required to reach this altitude?