Question

If a cylindrical tank holds 100,00 gallons of water which can be drained from thebottom of the tank in an hour, then Torricelli’s Law gives the volumeVof waterremaining in the tank aftertminutes asV(t) = 100,000(1−160t)20≤t≤60(a) What is the physical meaning ofV′(t)? What are the units?(b) Find and interpret the quantityV′(10).

Answer 1

Answer:

First, I think the right formula is:

$V(t) = 100,000(1-\frac{t}{60} ),20\leq t\leq 60$

A) We first derive the formula given above:

$V'(t)=-\frac{100000}{60}$

V'(t) represent the drain rate of the tank volume.

B) the units is: gallons/time

C) at V'(10) = 100000/60 = 1666.66 gallons/time.

because the formula V'(t) is constant so it doesn't depend of time.