Question

1. A baseball diamond is a square with a distance of 90 feet between the bases. A runner is running from first base to second at the constant rate of 20 feet per second. How fast is the distance between the runner and the catcher changing when the runner is halfway from first to second?

2. Water is dripping slowly onto a metal countertop, creating a circular wet spot whose area is increasing at the constant rate of ÆÄÀÌ/2 square inches per second. How fast is its radius increasin g when the radius is 4 inches?

3. An observer stands 25 feet from the base of a 50 foot flagpole and watches a flag being lowered at a rate of 5ft/sec. Determine the rate at which the angle of elevation from the observer to the flag is changing at the instant that the flag is 25 feet.

Answer 1

Let the distance from home to the runner be d.
Let the distance from first base to the runner be x

d^2 = 90^2 + x^2
2d dd = 2x dx

when x = 45, d = 45 sqrt(5) = 100.62

201.24 dd = 90 (20)
dd = 1800/201.24 = 8.94 ft/s

--------------------

can't read 2nd problem - font garbling

------------------

h/25 = tan(theta)
dh/25 = sec^2(theta) * dtheta

-5/25 = 2 * dtheta
-.1 = dtheta

Answer 2

For 2, I got 0.625 in/sec. dA/dt is pi/2.