Question 416419: A 5 gallon bucket is full of water at the bottom of the well. It is pulled to the top (100 ft) by winding a rope around an 18" diameter drum. If the rate of winding is 30-5t revolutions per minute, where t is minutes after we start, and the buckets leaks 1 gal/min, how much water is in the bucket at the top?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A 5 gallon bucket is full of water at the bottom of the well. It is pulled to the top (100 ft) by winding a rope around an 18" diameter drum. If the rate of winding is 30-5t revolutions per minute, where t is minutes after we start, and the buckets leaks 1 gal/min, how much water is in the bucket at the top?
..
let t=minutes it takes to pull 5 gal bucket to the top of the well
pi =3.14
18 inches = 1.5 ft
(30-5t)rev*min*1.5pi ft/rev
=(30-5t)1.5pi ft/min (speed at which bucket is being pulled)
distance=speed times travel time = 100 ft
(t)(30-5t)1.5pi=100
30*1.5pi t-5*1.5pi t^2=100
45pi t-7.5pit^2=100
9pi t-1.5pi t^2=20
4.71t^2-28.27t+20=0
use following quadratic equation to solve
..
..
a=4.71, b=-28.27, c=20
t=(28.7+-sqrt(28.7^2-4*4.71*20))/2*4.71
=(28.7+-21.14)/9.42)
t=5.29 min(time it takes to get bucket to top)
t=.8 min(reject, not reasonable)
ans:
If the 5 gal bucket leaks at a rate of gal/min, it would be empty when it gets to the top.
|
|
|
