Hello, ^_^Engineer_Adam^_^!

A baseball diamond is 90ft on a side.

A man runs from first base to second base at 25 ft/sec.

At what rate is his distance from the third base decreasing when he is 30ft from the first base? Of course, you made a sketch . . . Code:

B
*
* * x
* * A
90 * o
* o *
* o y *
C o *
* *
* *
* *
* *
* *
*

The man is at A.

His distance from second base is: .x = AB

. . That distance is decreasing at 25 ft/sec: .dx/dt = -25

His distance from third base is: .y = AC

. . We want dy/dt

From right triangle ABC, we have: .y² .= .x² + 90²

Differentiate with respect to time: .2y·(dy/dt) .= .2x·(dx/dt)

. . and we have: .dy/dt .= .(x/y)·(dx/dt) .**[1]**

When he is 30 feet from first base, x = __60__

. . And: .y² .= .60² + 90² . → . y = 30√13

And we know that: .dx/dt = -25

. . . . . . . . . . . . . . . . . . . . . . . . . . .__

Substitute into [1]: .dy/dt .= .60/(30√13) · (-25) .≈ .-13.9 ft.sec