Calculus

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A 15 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec.

Find the velocity of the top of the ladder at time t=2.

The velocity of ladder at time t=2 is ........ft/sec.

  • Calculus -

    let foot of ladder be x ft from wall
    let top of ladder by y ft above grouns
    x^2 + y^2 = 15^2
    2x dx/dt + 2y dy/dt = 0

    so when t = 2, x = 4+6 = 10
    y^2 = 225-100 = 125
    y = √125 , and dx/dt = 3

    2(10)(3) + 2(√125 dy/dt = 0
    dy/dt = -60/(2√125)
    = -30/√125
    = appr. -.2.68 ft/sec

    (the negative sign indicates the ladder is moving downwards)

  • ap wizardry -

    according to the ap wizardry handbook, using the demon spawn spell, the problem can be obliterated thorugh fire spitting dragons that originiate from the vave of JF.

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