# Drag on a ball - NewtonII & calculus

1. Oct 25, 2009

### Dan27

1. The problem statement, all variables and given/known data

A football of mass 0.4 kg travels horizontally above the ground. The ball experiences
a drag force of DT = 0.01v2 where v is instantaneous speed.
Immediately after the kick the ball has a speed of 15 m/s.
How long does it take for the speed to drop to 12 m/s?

2. Relevant equations

F = ma

0.01v2 = ma

0.01v2 = m(dv/dt)

3. The attempt at a solution

I realise that the acceleration is not constant and so Newton II will have to be used in creating a differential equation that can be integrated. But I'm struggling to take it from the differential with confidence in what I'm doing.

Can someone please let me know if i'm following the right lines and how to progress?

Cheers

2. Oct 25, 2009

### HallsofIvy

Staff Emeritus
Your equation is $-0.01v^2= .4\frac{dv}{dt}$ (".4" because you are given that m= .4 kg, "-" because drag is always opposite the direction of motion.).

You can "separate" that by multiplying both sides by -100dt and dividing both sides by $v^2$ to get $dt= -40v^2 dv$. Now integrate both sides.

3. Oct 25, 2009

### Dan27

That's brilliant thank you :)

I just assumed that I could neglect the negative by taking the acceleration or $\frac{dv}{dt}$ to also be negative?

Also, by dividing by $v^2$ would the RHS not be $\frac{-40}{v^2} dv$

Thank you!