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More Related Rates

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data

    2) One end of a rope is tied to a box. The other end is passed over a pulley 5 m above the floor and tied at a level 1 m above the floor to the back of a truck. The rope is L meters long. If the rope is taut and the truck moves at ½ m/s:
    a. How fast is the box rising when the truck is 3 m from point directly below the pulley?
    b. How far will the truck have to move to raise the box from the floor to a height of 2 m?

    2. Relevant equations

    Known:
    dx/dt = 0.5 m/s
    x^2 + 16 = z^2 (length of rope from pulley to truck)
    z + (5-y) = L (length of rope)

    3. The attempt at a solution

    for a:
    2x dx/dt = 2z dz/dt

    and dz/dt - dy/dt = 0, therefore dz/dt = dy/dt

    dy/dt = x/z dx/dt
    z = sqr (x^2 + 16)

    dy/dt = x/[sqr (x^2 + 16)]* 0.5, where x=3

    dy/dt = 0.3 m/s <---- someone verify?

    For part B: Not sure, just know that I need to find x, giving y.
     
  2. jcsd
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