Question

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 - 1/50t)2 0 < or = t < or = 50
1) Find the rate at which water is draining from the tank after the following amounts of time.
(a) 5 min gal/min
(b) 10 min gal/min
(c) 20 min gal/min
(d) 50 min gal/min
2) At what time is the water flowing out the fastest?
3) At what time is the water flowing out the slowest?

Answer 1

The response to this question can be defined as follows:

Explanation:

`v =4500 (1-(t)/(50))^2\\\\\to (dV)/(dt)= 9000 (1- (t)/(50))((1)/(50))\\\\`

`= 180 ((50-t)/(50))\\\\= 3.6(50-t)\\\\`

For point a:

`t=5\\\\V'=3.6* 45 = 162\\\\ans= - 162\ (gal)/(min)\\\\`

For point b:

`t=10\\\\V'=3.6* 40 = 144\\\\ans= - 144 \ (gal)/(min)\\\\`

For point c:

`t=20\\\\V'=3.6* 30 = 108\\\\ans= - 108 \ (gal)/(min)\\\\`

For point d:

`t=50\\\\V'=3.6* 0 = 0\\\\ans= 0 \ (gal)/(min)\\\\`