How do we calculate the rate of water level increase in a sloped swimming pool?

[Anabelle37]

URGENT - related rates pool problem

Homework Statement

A swimming pool with a rectangular surface 18 m long and 12m wide is being filled at the rate of 0.8 cubic metres/min. At one end the pool is 1m deep and at the other end it is 2.5m deep, with a constant slope between the ends. How fast is the height of the water rising when th depth of water at the deep end is 1m?

Homework Equations

The Attempt at a Solution

So i have dV/dt = 0.8 and i know i want to find dh/dt when h=1m from deep end.

dV/dt=dV/dh * dh/dt

The total volume of pool = 12*18*18*.5*1.5*18 = 52488 m^3

I'm having trouble working out the V in terms of h as the depth is different and different ends of the pool. Please help, this is for revision for an exam!

Thanks

 

[Mark44]

Homework Statement

A swimming pool with a rectangular surface 18 m long and 12m wide is being filled at the rate of 0.8 cubic metres/min. At one end the pool is 1m deep and at the other end it is 2.5m deep, with a constant slope between the ends. How fast is the height of the water rising when th depth of water at the deep end is 1m?

Homework Equations

The Attempt at a Solution

So i have dV/dt = 0.8 and i know i want to find dh/dt when h=1m from deep end.

dV/dt=dV/dh * dh/dt

The total volume of pool = 12*18*18*.5*1.5*18 = 52488 m^3

I'm having trouble working out the V in terms of h as the depth is different and different ends of the pool. Please help, this is for revision for an exam!

Thanks

Draw a side view of the pool, with the length being 18 m. and the depth being 1 m. at the shallow end and 2.5 m. at the deep end. The lower part of the side view is a right triangle that is 18 m. on one leg and 1.5 m. on the other. By using similar triangles you should be able to get a relationship between the depth of water and the length of the water line. (The width of the pool is always 12 m.)

 

[turbo]

I would like to ask why your homework questions are URGENT. Is there a good reason, other than procrastination and lack of effort? If so, maybe there is a way to get ahead of the curve on your work.

 

[Anabelle37]

Thank you Mark.

And turbo, it's urgent as I've tried to answer them and can't and don't want to just look them up online, I want to work them out myself and Physics Forums is good like that as it gives you hints but doesn't solve them for you. And it's for an exam in a few days and the lecturer does not give solutions out!

 

[Dick]

Thank you Mark.

And turbo, it's urgent as I've tried to answer them and can't and don't want to just look them up online, I want to work them out myself and Physics Forums is good like that as it gives you hints but doesn't solve them for you. And it's for an exam in a few days and the lecturer does not give solutions out!

Good answer.