For a particular stretch of highway illuminated by a row of identical lamps

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For a particular stretch of highway illuminated by a row of identical lamps, measurements show that at every moment the length ss (in metres) of a car’s shadow is 1.6 times the car’s distance dd (in metres) from the base of the nearest lamp. A car 1.4 m1.4\,\text{m} tall travels straight away from that lamp at a constant 22 m s−122\,\text{m}\,\text{s}^{-1}. (a) Using the relationship s=1.6ds = 1.6d, find dsdt\dfrac{ds}{dt} while the car is in motion. Give units. (b) Determine the speed of the tip of the car’s shadow at that same moment and express your answer with appropriate units.

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