Q16 of 43 Page 1

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


As per the Pythagoras Theorem,



∴ In right angled triangle - Δ ABC we have –


x2 + y2 = 52


Differentiating w.r.t t both sides -



⇒


⇒


When, x = 4 m


y2 = 25 – 16 = 9


∴ y = 3


Given, = 2 m/sec


∴ cm/sec


The height of the ladder on the wall is decreasing at the rate of cm/sec.


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