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N8G

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## Homework Statement

A professional thrower projects a football straight up in the air.

1. Assuming there is no air drag on the football, find the speed of the football as a function of height as the ball goes up.

2. Assuming the air drag on the football varies linearly with speed, find the speed of the football as a function of height as the ball goes up.

3. Assuming the air drag on the football varies quadratically with speed, find the speed of the football as a function of height as the ball goes up.

## Homework Equations

F=ma which extends to mv dv/dx through chain rule

linear drag = c1v

quadratic drag = c2v^2

In each case the sum of the forces in the y direction equals mg minus the corresponding drag term

## The Attempt at a Solution

1. mg = mv dv/dx ... separate variables, v(y) = root( 2gy +vo^2)

2. mg - c1v = mv dv/dx ... unsure how to isolate variables, haven't made it to part 3 but same issue

I'm hoping that I'm missing something simple that I've just overlooked, any help would be greatly appreciated.