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Differential problem solving

  1. Oct 4, 2007 #1
    1. The problem statement, all variables and given/known data

    A balloon is rising at a constant speed of 5ft/s. A boy cycling along a straight road at a speed of 15 ft/s. When he passes directly under the balloon, it is 45 ft above him. how fast is the distance between the boy and the balloon increasing 3 seconds later?

    2. Relevant equations

    s^2= x^2+y^2
    dx/dt = 15ft/s; dy/dt = 5ft/s

    3. The attempt at a solution

    2s(ds/dt)=2x(dx/dt)+2y(dy/dt)
    Now, the problem is, how do i find the general equation for me to pluck in the t?
     
  2. jcsd
  3. Oct 4, 2007 #2

    HallsofIvy

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    What do you mean by "the general equation"? You've already used the most general equation here- s^2= x^2+ y^2. You have, correctly 2s(ds/dt)+ 2x(dx/dt)+ 2y(dy/dt) (you might divide through by 2 to simplify.) You know dx/dt= 15 ft/s, dy/dt= 5 ft/s and certainly should be able to find x and y "3 seconds later" (how far does the boy go in 3 sec.? How far does the balloon rise in 3 sec.? And you can calculate s at that time. That's all you need.
     
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