Figure 1: Diagram without and with gravity

The models without and with gravity are illustrated in the figures above

for, and they can be described using the differential equations:

mv + um' = 0 and mv' +mg+um² = 0.

Solve both differential equations with respect to the speed v(t).

a) Without gravity. Solve the differential equation with respect to p'a the speed as a function of the mass.

b) With gravity. Solve the differential the speed as a function of time. equation with respect to p'a