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anonymous

  • one year ago

Applications to calculus Question: A ladder 26 feet long leans against a vertical wall. The foot of the ladder is being drawn away from the wall at the rate of 4 feet per second. How fast is the top of the ladder sliding down the wall when the foot of the ladder is exactly 10 feet from the wall?

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  1. amilapsn
    • one year ago
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    can you draw a sketch for this situation?

  2. anonymous
    • one year ago
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    |dw:1433325790037:dw|

  3. amilapsn
    • one year ago
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    |dw:1433326167643:dw|

  4. amilapsn
    • one year ago
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    so \(x^/(t)=4 m s^{-1}\) right?

  5. anonymous
    • one year ago
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    yeah that's right

  6. amilapsn
    • one year ago
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    so you need to find \(h^/(t)\).. What is the relation ship between x and h?

  7. anonymous
    • one year ago
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    I tried representing this question by using Pythagoras.

  8. amilapsn
    • one year ago
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    good..

  9. anonymous
    • one year ago
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    So given x' = 4ft/sec I ended up having something like this: z(t)^2 = x(t)^2 + y(t)^2

  10. amilapsn
    • one year ago
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    so what would the next step be?

  11. anonymous
    • one year ago
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    I derived So I ended up with this: 2z(t)dz = 2 x(t) dx + 2 y(t)dy dt dt dt

  12. amilapsn
    • one year ago
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    what would be the value of dz/dt?

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