A question in a book about ordinary differential equations states:
"An object of mass m is thrown vertically upwards. The air resistance is proportional to the square of the velocity. Derive the differential equation relating the velocity v and time."
When I drew a diagram of a ball being thrown upwards I drew onto it an arrow pointing downwards marked mg.
Now there would also have to be another arrow marked on the diagram to indicate air resistance and I would imagine this would also point downwards.
In the book the answer is given as m(dv/dt) + kv^2 = mg
I know they have first calculated the net forces acting on the body, and then used F=ma
Does anyone know how they got this asnwer? Thanks very much!
Differential Equation watch
- Thread Starter
- 06-04-2011 20:03
- 06-04-2011 20:49
- 07-04-2011 04:14
The book's wrong. kv^2 and mg should have the same sign. It should read m(dv/dt) + kv^2 + mg = 0
- 07-04-2011 04:26