Draw a diagram. It is clear that when the batter has gone x feet, his distance z from 2nd base is
z^2 = (90-x)^2 + 90^2
so,
2z dz/dt = 2(x-90) dx/dt
so, figure z when x=45 and plug in the numbers
The distance from 3rd base is very similar.
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 19 ft/s.
(a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.)
ft/s
(b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.)
ft/s
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