A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall??

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Answer 1 · 2017-07-30T13:29:48

The height is decreasing at the rate of #=2.67cms^-1#

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Here , we apply Pythagoras

#x^2+y^2=L^2#

Differentiating with respect to #t#

#2xdx/dt+2ydy/dt=0#

#dx/dt=0.02ms^-1#

#x=4m#

#y=sqrt(5^2-4^2)=sqrt(25-16)=sqrt9=3#

Therefore,

#dy/dt=-x/ydx/dt=-4/3*0.02=-0.0267ms^-1#