Homework SourseA baseball diamond is a square 90 feet on each side A player
A baseball diamond is a square 90 feet on each side. A player is running from home to first base at the rate of 20 feet per second. At what rate is his distance from second base changing when he is 45 feet from first base? (Round your answer to three decimal places.)
Solution
sol In your case, the orientation is different, but the situation is the same. we have You want the rate of change of the diagonal which has as its length the square root function. then For you, the guy is going the other way, so x is decreasing, and the the value you are interested in is 45. Let me know if you need further clarification. distance to second base is sqrt( x^2 + 8100). and x = 90 - 25t for t seconds so we have sqrt( (90 - 25t)^2 + 8100) Derivative of that with respect to t is (125*t-450) / sqrt( 25*t^2 - 180*t + 648 ) x = 45 = 90 -25t t = 45/25 so Evaluating the derivative we have: -11.1803399 ft/second, which meaning the distance is decreasing by that amount.
