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Math Help - Calcccc R.Rates

  1. #1
    Newbie Jason2JZ's Avatar
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    Calcccc R.Rates

    Two Cyclists depart at the same time from a starting point aloing routes that make an angle 60 degrees with each other. the first cyclist is travelling at 15km/h while the second is moving at 20km/h. how fast are the cyclist moving apart after 2 hours?
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  2. #2
    Eater of Worlds
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    For this one we do not have a right triangle. We have an angle of {\theta}=\frac{\pi}{3}

    We can use the law of cosines.

    Draw the diagram. It'll help.

    Let \frac{da}{dt}=15 be the rate of one biker and

    \frac{db}{dt}=20 be the rate of the other.

    In two hours, one biker will have traveled 15*2=30 km

    and the other will have traveled 20*2=40 km

    So, we have a whole bunch of info to enter into the law of cosines formula after it is differentiated.

    We need dc/dt.

    Use the law of cosines to find c with a=30, b=40, theta=Pi/3

    c^{2}=a^{2}+b^{2}-2ab\cdot cos({\theta})

    Remember, the bikers maintain a constant angle, so \frac{d{\theta}}{dt}=0. That makes it easier.

    Now, go for it. You have all you need. If you get hung up, let me know.
    Attached Thumbnails Attached Thumbnails Calcccc R.Rates-bikers.gif  
    Last edited by galactus; December 7th 2008 at 02:24 PM.
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