Calculus

posted by Stuck

"At 9am ship A is 50 km east of ship B. Ship A is sailing north at 40km/h and ship B is sailing south at 30km/h. How fast is the distance between them changing at noon?"

I can never get these type of questions where two ships are heading in different directions and one is always ahead...please help!

  1. Reiny

    For most of these, the key is to have a good diagram.
    In this problem I would place B at the origin and A on the 50 axis somewhere.
    label AB as 50
    draw a vertical up from A to C to show the path of A
    Draw a vertical down from B to D to show the path of B
    Join DC, this is our distance between them.
    Now we need a righ-angled triangle, so extend CA to E so that AE = BD. Join DE

    Let t hours be any time after 9:00 am
    then BD = 30t and AC = 40t, making CE = 70t
    We know DE = 50
    DC^2 = CE^2 + DE^2
    = 4900t^2 + 2500
    differentiate with respect to t
    2 DC (dDC/dt) = 9800t
    dDC/dt = 9800t/2DC
    when t- 3 (noon)
    DC^2 = 4900(9) + 2500
    DC = 215.87

    so dDC/dt = 9800(3)/(2(215.87)) = 68.1 km/h

  2. Quidditch

    This same question was answered Wednesday for your 10:58pm post.

    Check back a few pages to see it.

  3. Stuck

    Thank you both! However, the problem is I can't seem to visualize the diagram correctly. I can't see where the right triangle is coming from. But no worries, I will look at more example problems and see if I can figure these questions out.

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