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10/A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulledalong the ground, away from the wall, at the rate of 2cm/s. How fast is its heighton the wall decreasing when the foot of the ladder is 4 m away from the wall |
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Answer» length of ladder is l=5mwhen distance(x )of ladder from wall is 4m its height(h) on wall=(l^2 -x^2)^0.5h=(25-16)^2=3mgiven dx/dt =-2cm/s=-0.02m/snow;h^2 =l^2 -x^2differentiating w.r.t. to time t2h dh/dt =0-2x dx/dtputting values 2×3 dh/dt = -2×4×(-0.02)6 dh/dt = 0.16dh/dt =0.08/3 cm/s=8/3 m/s |
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