The rate of increase of length of the shadow of a man meters height, due to a lamp at meters height, when he is moving away from it at the rate of is:

Explanation: Solution: 1. Define the Variables: Let be the height of the lamp post . Let be the height of the man . Let be the distance of the man from the lamp post. Let be the length of the man's shadow. 2. Given Information: The man is moving away from the lamp post at a rate of . Therefore, . We need to find the rate of increase of the shadow length, which is . 3. Set up the Equation: Using the property of similar triangles from the geometry of the situation: 4. Simplify the Relation: Cross-multiply to solve for the relationship between and : 5. Differentiate with respect to time ( ): Substitute the given value : Correct Option: (a)

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