Question

A baseball diamond is a square with side lengths of 90 ft.  A batter hits the ball and runs toward first base at a rate of 26 ft/s.  At what rate is the distance between the batter and second base decreasing when the batter is half way to first base?  Let  x be the distance between the batter and first base,  y be the distance between first base and second base, and  z be the distance from second base to the batter.  All distances are measured in feet.

a. What equation relates x, y, and z? b. Is x getting bigger or smaller? Select an answer du dt ft/s d. dy dt ft e. What is z when the batter is halfway to first bast? Select an answer f. Implicitly differentiate the equation from part "a" with respect to time. Do not simplify. dz dz g. Solve for and simplify. dt dt h. At what rate is the distance between the batter and second base changing by? Select an answer dz dt

Answer 1