Example 44 - A man of height 2 meters walks at uniform speed - Finding rate of change

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 44 A man of height 2 meters walks at a uniform speed of 5 km/h away from a lamp post which is 6 meters high. Find the rate at which the length of his shadow increases. Let AB be the lamp post & Let MN be the man of height 2m. & Let AM = l meter & MS is the shadow of the man Let length of shadow MS = s Given man walks at speed of 5 km/h ∴ ﷐𝑑𝑙﷮𝑑𝑡﷯ = 5km/h We need to find rate at which the length of his shadow increases. i.e. we need to find ﷐𝑑𝑠﷮𝑑𝑡﷯ From (1) & (2) ﷐6﷮1000 ﷐𝑙 + 𝑠﷯﷯ = ﷐2﷮1000﷐𝑠﷯﷯ ﷐6﷮𝑙 + 𝑠﷯ = ﷐2﷮𝑠﷯ 6s = 2l + 2s 6s – 2s = 2l 4s = 2l 2s = l l = 2s We need to find ﷐𝑑𝑠﷮𝑑𝑡﷯ Diff w.r.t t ﷐𝑑𝑙﷮𝑑𝑡﷯= ﷐𝑑﷐2𝑠﷯﷮𝑑𝑡﷯ ﷐𝒅𝒍﷮𝒅𝒕﷯= 2.﷐𝑑𝑠﷮𝑑𝑡﷯ 5 = 2 ﷐𝑑𝑠﷮𝑑𝑡﷯ ﷐𝑑𝑠﷮𝑑𝑡﷯ = ﷐5﷮2﷯ So, ﷐𝒅𝒔﷮𝒅𝒕﷯ = ﷐𝟓﷮𝟐﷯ km/hr.

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