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July 23rd, 2012, 07:03 PM   #1
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Rate of change of distance

If anyone could help me with this problem, I'd greatly appreciate it. I honestly don't even know how to start this one, can't find any similar examples in my notes, and will need to do one just like this on a test tomorrow. Any help is greatly appreciated.

A (square) baseball diamond has sides that are 90 feet long. A player 20 feet from third base is running at a speed of 21 feet per second. At what rate is the player's distance from home plate changing? (Round your answer to two decimal places.)
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July 23rd, 2012, 07:58 PM   #2
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Re: Rate of change of distance

I drew a rough sketch:

[attachment=0:2oi6r39t]baseballplayer.jpg[/attachment:2oi6r39t]

The player is at point P and his velocity has been resolved into its x and y components to the right.

The player is running along the line and his distance D from home plate H is:



Substitute for y:



Differentiate with respect to time t:



When the player is 20 feet from 3rd base, his x-coordinate is and we have:

hence:

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July 24th, 2012, 03:09 PM   #3
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Re: Rate of change of distance

A simpler approach:

Orient the diamond such that 3rd base is at the origin and home plate is at (0,-90) and the player is then running along the x-axis.

Suppose the player is at (x,0) and we are told

The distance between the player and home plate is therefore:



hence, differentiating with respect to t:



When the player is 20 ft from home base, i.e., x = 20, we find:

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A (square) baseball diamond has sides that are 90 feet long. A player 20 feet from third base is running at a speed of 29 feet per second. At what rate is the player's distance from home plate changing? (Round your answer to two decimal places.)
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