# Math question

1. May 10, 2005

### Logistics

I have a major exam coming up and we've been given few past exam papers to go through to practice.

I have absolutely no idea what to do here , if people could help me out, work it out etc. It would be greatly appriciated.

Thanks

Last edited: May 10, 2005
2. May 10, 2005

### Zurtex

3. May 10, 2005

### Logistics

Last edited: May 10, 2005
4. May 10, 2005

### A_I_

i might help you somewhat although i haven't got the complete solution:

you know that the volume of a cylinder is given by: V= Ah (where A is the area of the base).

so when deriving with respect to time ull have:
dV/dt = A*dh/dt

and given (from Toricelli's law) that dV/dt = -a*squared root(2gh)

you can set the two equalities and obtain:

dh/dt = (-a/A)*squared root(2g)*squared root(h)

therefore the alpha constant should be equal to the rate of the samller area (the circular hole) to the bigger area (the one of the cylinder base) times the squared root of 2g's.
that's for the first part.

for the second part you will have to integrate the squared root of h knowing that -alpha is a constant.

As for the third it's a numeral application for the second part.

I hope this helped.

5. May 10, 2005

### Logistics

Thank you very much.

I have worked it all out :)

3 questions left that I don't understand will post them later :p