RELATED RATES 0 99
An open pipe with length 3 meters and outer radius of 10 centimeters has an outer layer of ice that is melting at the
rate of 2ir cm
3 /min. How fast is the thickness of ice decreasing when the ice is 2 centimeters thick?
I Let x be the thickness of the ice. Then the volume of the ice V = 300[Tr(10 + xf - lOOir], So D,V =
300ir[2(10 + x)• D,x]. Since D,V= -2ir, we have -277 = 600ir(10 + x)• D,x, D,x = -I/[300(10 + x)].
When x = 2, D t x = — 3555 cm/min. So the thickness is decreasing at the rate of 5^5 centimeter per minute
(4 millimeters per day).
Fig. 14-24
14.55
In Fig. 14-24, a baseball field is a square of side 90 feet. If a runner on second base (II) starts running toward
third base (III) at a rate of 20 ft/s. how fast is his distance from home plate (//) changing when he is 60 ft from II?
Let x and u be the distances of the runner from III and H, respectively. Then u
2 = x
2 + (90)
2
,
14.56
When x=90-60=30,
therefore.