Question

A model for a ball thrown into the air with air resistance proportional to the velocity is given by dv dt = −g−cv. Solve for v and the position of the ball when c = 0.05.Assume that g = 32 ft/sec2.

Please use ordinary differential equation to solve.

Answer 1

The differential equation is:

This can be solved as:

For the position, we do:

where are constants which can be found from initial conditions. Given the values of and , we can write:

Assuming that the ball is thrown from , we get:

Then: