206
3.5. RELATED RATES
3. A baseball diamond is a square with sides 90 feet long. Suppose a baseball player is
advancing from second to third base at the rate of 24 feet per second, and an umpire is
standing on home plate. Let θ be the angle between the third baseline and the line of
sight from the umpire to the runner. How fast is θ changing when the runner is 30 feet
from third base?
4. Sand is being dumped off a conveyor belt onto a pile in such a way that the pile forms
in the shape of a cone whose radius is always equal to its height. Assuming that the
sand is being dumped at a rate of 10 cubic feet per minute, how fast is the height of the
pile changing when there are 1000 cubic feet on the pile?
3.5. RELATED RATES
3. A baseball diamond is a square with sides 90 feet long. Suppose a baseball player is
advancing from second to third base at the rate of 24 feet per second, and an umpire is
standing on home plate. Let θ be the angle between the third baseline and the line of
sight from the umpire to the runner. How fast is θ changing when the runner is 30 feet
from third base?
4. Sand is being dumped off a conveyor belt onto a pile in such a way that the pile forms
in the shape of a cone whose radius is always equal to its height. Assuming that the
sand is being dumped at a rate of 10 cubic feet per minute, how fast is the height of the
pile changing when there are 1000 cubic feet on the pile?