anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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amilapsn
  • amilapsn
can you draw a sketch for this situation?
anonymous
  • anonymous
|dw:1433325790037:dw|
amilapsn
  • amilapsn
|dw:1433326167643:dw|

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amilapsn
  • amilapsn
so \(x^/(t)=4 m s^{-1}\) right?
anonymous
  • anonymous
yeah that's right
amilapsn
  • amilapsn
so you need to find \(h^/(t)\).. What is the relation ship between x and h?
anonymous
  • anonymous
I tried representing this question by using Pythagoras.
amilapsn
  • amilapsn
good..
anonymous
  • anonymous
So given x' = 4ft/sec I ended up having something like this: z(t)^2 = x(t)^2 + y(t)^2
amilapsn
  • amilapsn
so what would the next step be?
anonymous
  • anonymous
I derived So I ended up with this: 2z(t)dz = 2 x(t) dx + 2 y(t)dy dt dt dt
amilapsn
  • amilapsn
what would be the value of dz/dt?

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