Mathematics OpenStudy (anonymous):

I know this is a Pythagorean based solution, but I must be setting something up wrong because I can't get the answer to make sense... A baseball player runs from home plate towards first base at 20 ft/s. How fast is the player's distance from second base changing when the player is one-third of the way to the first base? (One side of a baseball diamond is 90 ft. Round your answer to two decimal places.) I've tried it implicitly from 90=sqrt(z^2-x^2) and from z^2=x^2+90^2 and got two different answers, so I know I am setting it up wrong, or dropping something. can someone step me through it?I know this is a Pythagorean based solution, but I must be setting something up wrong because I can't get the answer to make sense... A baseball player runs from home plate towards first base at 20 ft/s. How fast is the player's distance from second base changing when the player is one-third of the way to the first base? (One side of a baseball diamond is 90 ft. Round your answer to two decimal places.) I've tried it implicitly from 90=sqrt(z^2-x^2) and from z^2=x^2+90^2 and got two different answers, so I know I am setting it up wrong, or dropping something. can someone step me through it? OpenStudy (precal):

related rates calculus problem OpenStudy (amistre64):

|dw:1319630889709:dw| OpenStudy (amistre64):

its pythag alright, and its related to the top portion as the distance from h to 1 shrinks at a rate of 20 OpenStudy (amistre64):

(h2)^2 + (h1)^2 = (dr)^2 h2^2 + (90-r)^2 = dr^2 2 h2 h2' + 2(90-r)* -r' = 2 dr dr' h2' never moves so it 0; r' is our 20, and the distance run so far is 30 so lets fill those in.. 2 h2 0 + 2(90-30)* -20 = 2 dr dr' 120* -20 = 2 dr dr' 120* -10 = dr dr' -1200 = dr dr' now all you gotta do it determine the distance from 2base to the runner and plug it in to solve for dr' OpenStudy (amistre64):

it a cursory glance id say that dr^2 = 90^2 + 60^2 such that dr = sqrt(11700) that gives me an answer of -11.094 ft per sec. OpenStudy (precal):

Yes but related rates is where calculus and implicit and geometry are combined. So it is strictly pythagorean, no OpenStudy (amistre64):

whereever you have related rates you can do calculus, implicit is just another form, per se, of the calculus. The pythag is the relation we can use in this example to aid us. OpenStudy (amistre64):

is it strictly pythag? no, and im sure there are other ways to relate it, but the pythag seems to work easiest to me OpenStudy (precal):

yes but all related rates problems involve some formula from geometry. OpenStudy (amistre64):

the easy ones from the text book do yes :) OpenStudy (precal):

ok you win..... that is the thing about math....you can always find some hard problem that takes time to solve..

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