Determine how fast the top of the ladder is decreasing when the foot of the ladder is 3 meters from the house.
A 5 meter long ladder is leaning against the side of a house. the base of the ladder is pulled away from the house at a rate of .4m/sec. Determine how fast the top of the ladder is decreasing when the foot of the ladder is 3 meters from the house. List the unknown,constant and given
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Let the base of the wall be at the origin, the distance from the foot of the wall be `x` , and the height where the ladder meets the wall be `y` .
Since the ladder is 5m long, the pythagorean theorem gives us :
`x^2+y^2=25` . We are given `x=3m,(dx)/(dt)=.4m/sec` and we are wanting to compute `(dy)/(dt)` .
Differentiate with respect to `t` :
`2x (dx)/(dt)+2y(dy)/(dt)=0` . Now `x=3 =>y=4` and `(dx)/(dt)=.4` ;substituting these values gives us:
So when the base of the ladder is 3m from the wall, the top of the ladder is sliding down the wall at a rate of .3 m/sec.
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