rates question (1 Viewer)

[Grey Council]

Hey,

Started this today, finished it today. Can't seem to see what I'm doing wrong with this qusetion though:

A Horizontal Trough 10m long, has a cross-section in the shape of a right-angled isosceles traingle. If water is poured in at the rate of 8m^3 / min, at what rate is the water level rising when the depth of the water is 2m?

I keep getting 2/5m / min and in the answers it says 1/5m / min.

 

[wogboy]

Whenever the water in the horizontal trough is at height x, the volume of water V is (all units are in metres and minutes):

V = 10x^2 ...(A)

(multiply the cross sectional area of the right isosceles triangle, by the length of the trough which is 10)

The inflow rate is:
dV/dt = 8

from (A),
dV/dx = 20x

so,
dx/dt = (dV/dt)/(dV/dx)
= 2/(5x)

so when x = 2,
dx/dt = 2/10
= 1/5 metres/minute

so the water rises at 1/5 metres/minute.

 

[Grey Council]

ummm, i think I went wrong in the volume of the whole darn thing. Isnt the volume of a trough (a traingular prism, or cylinder, or whatever the heck its damn called) the area of triangle times 10?

V = 10x^2 ...(A)

I had volume of right angled isosceles triangle times 10 as being:
x^2/2 * 10 = 5x^2

dV/dX = 10x
dV/dt = 8 m^3 / min

8/10x = dx/dt , where x = 2

so 2/5 m/min.

umm, doing something wrong, most prolly volume of the shape.

 

[Xayma]

Yeah you are doing the volume wrong, the depth of the water is x metres. You are taking one of the isoceles sides as x.

See the attachment:

The triangle off the side is a rightangles isosceles triangle with lengths x,x, sqrt(2) x.

Since the sqrt(2) x side is the smaller side on the main traingle we get A=1/2 ab Sine C
A= 1/2.2x².1
A=x²
then times by 10 to get the volume

Or since the base of the triangle will be 2x use A=1/2bh.

 

[Grey Council]

o! Thanks mate.

 

[Grey Council]

btw, can someone please refer me to or post up an example of a question which is pretty much the hardest they can ask us? A Rates question, I mean.

 

[Supra]

oi guardian where did u get that question from?

 

[Grey Council]

its in the couchman, coroneos, and the fitzpatrick (i think).

 

[Supra]

I knew that question looked familiar!!!, i stuffed up on it as well, it took me ages to find out where i went wrong, but this happened way back in yr11
I use couchman btw

 

[Grey Council]

oo k.

Can't someone please give me a few really hard 3u rates questions?

 

[Grey Council]

please