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Hitting a double


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Suppose a baseball player runs at a speed of 24 ft/s. He is trying to run on a baseball field where it's 90 feet to each base.  Determine the rate of change to second base once the runner reaches halfway to first base. 

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  1. "Determine the rate of change to second base once the runner reaches halfway to first base." 
     
  2. Determine the time rate of change of the distance between the runner and 2nd base when the runner is halfway between home plate and first base, running at 24 ft/sec on a path that is a straight line from home plate to first base.

If these two statements ask for the same information, then

Spoiler

The component of the runner's speed in the direction of 2nd base would be cos (arctan (2)) = .44721.
That portion of 24 ft/sec is 10.733 ft/sec.

 

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