Application of DerivativeMedium

Question

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 m/sec. How fast its height on the wall decreasing when the foot of the ladder is 4 m away from the wall-

Options

A.4/3 m/sec
B.8/3 m/sec
C.10/3 m/sec
D.6/3 m/sec

Solution

    
Let at time t, the lowers end P of ladder PQ be at a distance x meters from the wall and the upper end Q be at height y from the ground.
Then x2 + y2 = 25
∵      = 2
we find  when x = 4
On putting x = 4 in x2 + y2 = 25
we get y = 3
Now x2 + y2 = 25
⇒ 2x + 2y  = 0
⇒ 2 . 4 . 2 + 2 .  = 0
⇒  m/sec
Hence its height on the wall decreasing at the rate of  8/3 m/sec.

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