Page 146 - Calculus Workbook For Dummies

130 Part III: Differentiation

7. A six-foot tall man looking over his 8. Salt is being unloaded onto a conical pile at
shoulder sees his shadow that’s cast by a a rate of 200 cubic feet per minute. If the
15-foot tall lamp post in front of him. The height of the cone-shaped pile is always
shadow frightens him so he starts running equal to the radius of the cone’s base, how
away from it — toward the lamp post. fast is the height of the pile increasing
Unfortunately, this only makes matters when it’s 18 feet tall?
worse, as it causes the frightening head of
the shadow to gain on him. He starts to Solve It
panic and runs even faster. Five feet before
he crashes into the lamp post, he’s running
at a speed of 15 miles/hour. At this point,
how fast is the tip of the shadow moving?

Solve It