Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.(adsbygoogle = window.adsbygoogle || []).push({});

(In case you're wondering, I'm doing my studies by correspondence, so other than course notes and textbooks borrowed from the library I have just the internet and my brains (hah!) to aid me)

1. The problem statement, all variables and given/known data

A baseball diamond has sides 27m long. A player is running from 2nd to 3rd at a speed of 9m/s. When he is 6m away from 3rd, at what rate is the player's distance from home plate changing at that instant?

3. The attempt at a solution

x = distance from home plate to 3rd = 27m

y = distance from player to 3rd = 6m

z = distance from player to home = 27.66m (using pythagoras)

speed of player is change of y over time: dy/dt = 9m/s

[tex]z^{2}[/tex] - [tex]y^{2}[/tex]= [tex]x^{2}[/tex]

differentiate with respect to time:

d/dz[tex]z^{2}[/tex] - d/dy[tex]y^{2}[/tex]= 0 (since x doesn't change over time)

dz/dt*2z - dy/dt*2y = 0

divide by 2:

z*dz/dt - y*dy/dt = 0

sub the above (z, y, dy/dt) into the equation and solve:

dz/dt = 1.95m/s

If this ain't correct, please tell me quickly as I need to post my assignment off asap!

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# Rate of change in distance question

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