SOLUTION: A baseball diamond has the shape of a square with sides 90 ft. long. A player 60 ft from second base is running towards third base at a speed 28 ft/min. At what rate is the players
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Question 1117083: A baseball diamond has the shape of a square with sides 90 ft. long. A player 60 ft from second base is running towards third base at a speed 28 ft/min. At what rate is the players’ distance from the home plate changing?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
A related-rates problem.
Let 3rd base be at the origin, 2nd base at (0,90) and H the home plate along the x-axis at (90,0).
r is the distance from the runner to home plate.
Instantaneous values at t=t0:
y(t0) = 30 ft
r(t0) = ft
dy/dt = -28ft/min (negative because the direction is down the y-axis, so y values are getting smaller)
The problem asks you to find dr/dt.
r = where r=r(t), x=x(t), y=y(t)
Since x(t) is a constant (H is at (90,0), so the x distance is 90ft), we have
r =
Differentiating both sides WRT t:
dr/dt =
dr/dt = ft/min
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