Thread: related rates help:

A baseball diamond is 90ft on a side. (It is really a square). 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?

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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