A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) At what rate is his distance from second base decreasing when he is halfway to first base

13.86 ft/sec

Step-by-step explanation:

If we let x = distance batter has run at time t and  D = distance from second base to the batter at  time t, then we know and we want when he is halfway (at x = 45).

Using Pythagoras theorem

When x=45

Thus, when the batter is halfway to first base, the distance between second base and the batter is  decreasing at the rate of about 13.86 ft/sec.