July 23rd, 2012, 07:03 PM  #1 
Senior Member Joined: Jun 2011 Posts: 154 Thanks: 0  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.) 
July 23rd, 2012, 07:58 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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 xcoordinate is and we have: hence: 
July 24th, 2012, 03:09 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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 xaxis. 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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