Assume the motion occurs under constant gravitational acceleration g, and that the initial velocity of the rocket on the surface of the earth is zero. Find the greatest speed achieved and the greatest height reached under that condition. Assume a and m are both constant in time. Assume that the motion occurs under constant gravitational acceleration g , and that friction can be neglected. Set up the equation of motion and integrate it under the assumption that the initial velocity of the rocket on the surface of the earth is zero.
Moisture condenses at the constant rate l units of mass per unit time on a falling raindrop.
Neglect air resistance. As a result of condensation, the water drop experiences a continuous increase in mass, proportional to its surface. Its radius r then increases linearly with time. Integrate the differential equation of the motion by introducing r instead of t as independent variable. The rain fills the cars at a constant rate of l mass units per unit time.