Choose the correct option from the given alternatives : A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of (1.5 "m")/sec. The length of the higher point of ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of

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2 Explanation: Given L = 5 m, dx/dt = (1.5 "m")/sec and x = 4 using pythagoras theorem, x2 + y2 = L2 ...(1) differentiating both sides w.r.t 2xdx/dt + 2y dy/dt = 0 dy/dt = -x/y dx/dt at x = 4, y = sqrt("L"^2 - x^2) = sqrt(5^2 - 4^2) = 3m. $\therefore$ dy/dt = -$\frac{4}{3}$ xx 1.5 = (-4)/3xx3/2 = - 2 m/sec Hence, it Decreases at the rate of 2m/sec. $\therefore$ So, 2m/sec is correct answer.

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