# Calculus-Related Rates

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Three elementry kids are at a field day hula hoop contest. They were the last one standing of the heated competition. They have been hula hooping for 10minutes. Student1 (S1) is at point (6,5); Student2 (S2) is at point (6,1) while student 3(S3) is at (1,1). Finally, the gym teacher yelled \"Attack!\" and S1 and S2 started moving towards S1 who has weak legs started moving back at 1.5 ft/sec and finally fell. If S2 and S3 moved at .7ft/sec what is the angle between s2,s3 and where s1 fell.

• Calculus-Related Rates -

draw this on grid paper. make theta the angle you are interested in. You know three sides, and the derivative of a couple of those (dx/dt) and dy/dt)..check the diagram.

Now, use the law of cosines:
c^2=a^2+b^2-2ab cosTheta

take the derivative with respect to time.

2c dc/dt= 2a da/dt+2bdb/dt -2

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