If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V = 4500 (1 - 1 / 50 t) ^2. 0≤ t ≤ 50. At what time is the water flowing out the fastest?

Question

Louis Davenport

Mathematics

3 December, 14:13

If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V = 4500 (1 - 1 / 50 t) ^2. 0≤ t ≤ 50. At what time is the water flowing out the fastest?

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Answers (1)

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Hodges · Answer 1

t = 0

Before it starts rushing that's when it will be fastest

Step-by-step explanation:

For the water ib the tank to flow very fast it means that there is a big volume of water present.

And for volume of water to be present that much it means that the water must

have not leaked much or at all.

And for that it signifies large volume of water.

If we do the calculation we'd see that time will be actually equal to zero for the pressure and the volume of the water to be biggest.

V = 4500 (1 - 1 / 50 t) ^2

V = 4500

4500 = 4500 (1 - 1/50t) ²

1 = 1 - 1/50t

0 = - 1/50t

t = 0