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(It's a related rate question)

A man 6ft tall walks away from a lamp post (15ft) at 5ft/sec. How fast is his shadow lengthening?


I have the picture, and the constants, the man and the lamp post. I have 5ft/sec as dw/dt, and I know I'm looking for ds/dt, the rate of the shadow.

Problem is, I don't know the actual equation to figure this out. Help please?


  • Calculus -

    The lamp post makes a right triangle.

    let x be the distance from the lamppost to the man (dx/dt=5; given) Let L be the length of is shadow, measured from the man feet to the end of the shadow.
    (dL/dt is the rate of the shadow lengthens.

    Using similar triangle
    6/15=L/(L+x) or
    6x=9 L
    x=3/2 L
    dx/dt= 3/2 dL/dt
    well, then dL/dt=2/3 dx/dt= 2/3 5=10/3 ft/sec

    Now if you were to ask at what rate the shadow tip was moving , that is dx/dt+dL/dt

  • Calculus -

    let x be the rate of shadow.

    x / (x + 5) = 6 / 15
    15x = 6(x+5) = 6x + 30
    9x = 18
    x = 30/9 = 10/3

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