Explanation Given: From Figure 1, it is observed that the spot is at a distance of 40 ft from the shore. The closest point to the shore from the place of the man is at a distance of 40 ft. The speed of the man on the shore is 5 ft per second. The speed of paddling is 3 ft per second. Calculation: Let 40 − x be the distance that the man travels on the shore. Then x is the distance that he does not travel along the shore. Applying Pythagorean Theorem for the given figure, The distance that he travel in water is x 2 + 40 2 = x 2 + 1600 . The formula for time taken is t = d r where d is distance and r is rate of speed. The time taken by him to travel along the shore is 40 − x 5 . The time taken by him to travel in the water is x 2 + 1600 2 . The total time is, T ( x ) = 40 − x 5 + 1600 + x 2 3 = 40 5 − x 5 + 1600 + x 2 3 = 8 − x 5 + 1600 + x 2 3 Find the critical points by evaluating T ′ ( x ) and equating to 0. T ′ ( x ) = − 1 5 + 1 3 ( 1 2 ) ( 2 x ) ( 1600 + x 2 ) − 1 2 = − 1 5 + x 3 ( 1600 + x 2 ) − 1 2 Equate T ′ ( x ) to 0

11th Edition

ISBN: 2818440028625

Author: Lial

Publisher: ELSEVIER

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Chapter 6, Problem 67RE

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Chapter 6, Problem 66RE

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