A swimming pool is 50m long and its depth decreases linearly along the length fr

Question

A swimming pool is 50m long and its depth decreases linearly along the length from 3m to 1m. Initially the swimming pool is empty.

1) Suppose the width of the swimming pool is 20 m wide and the water fills at a rate of 1m^3/min.

a) How fast is the water level raising 200 minutes after filling begins?

b) How fast is the water level raising 1250 minutes after filling begins?

c) How long will it take the swimming pool to fill?

2) Suppose the width of the swimming pool is 20 m wide and the water fills at a rate of 2m^3/min.

a) How fast is the water level raising 200 minutes after filling begins?

b) How fast is the water level raising 600 minutes after filling begins?

c) How long will it take the swimming pool to fill?

3) Suppose the width of the swimming pool is 40 m wide and the water fills at a rate of 1m^3/min.

a) How fast is the water level raising 200 minutes after filling begins?

b) How fast is the water level raising 2200 minutes after filling begins?

c) How long will it take the swimming pool to fill?

4) Suppose the width of the swimming pool is 40 m wide and the water fills at a rate of 2m^3/min.

a) How fast is the water level raising 200 minutes after filling begins?

b) How fast is the water level raising 2200 minutes after filling begins?

c) How long will it take the swimming pool to fill?

Explanation / Answer

at any length l

the volume(V) = 0.5*l*(1+2l/50)*width

a) 200m will make 200m^3 water = 0.5*l*(1+2l/50)*width

20 = l*(1+0.04l)

get value of l

dV/dt = (0.5*{(1+2l/50) + 2l/50}*20)*dl/dt = 1

put l vlue in this

this will give you dl/dt

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