a. Explanation Given: The air pressure (in atmospheres) at a height of s meters above sea level is given by, p ( s ) = e − 0.000125 s Also, the position of the box above the sea level aftert sec is: s ( t ) = 3000 − 49 t − 245 ( e − t 5 − 1 ) Formula used: d d x ( x n ) = n x n − 1 d d x ( e a x ) = a e a x d d x ( f ( x ) + g ( x ) ) = d d x ( f ( x ) ) + d d x ( g ( x ) ) By chain rule: d d t f [ u ( x ) ] = d d u f ( u ) d u d x Calculations: Now, by chain rule, the rate of change of air pressure with respect to time is, d p d t = d p d s ⋅ d s d t Consider, d p d s = d d s ( e − 0.000125 s ) = − 0.000125 e − 0 b. To determine To find: the time when box hits the water and the rate of change of air pressure at the time of impact.

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 3.7, Problem 49PS

To determine

To find: dsdt andthe rate of change of air pressure2 seconds after box begins to fall.

To determine

To find: the time when box hits the water and the rate of change of air pressure at the time of impact.

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Chapter 3.7, Problem 48PS

Chapter 3.7, Problem 50PS

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Student's Solution and Survival Manual for Calculus

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d s d t andthe rate of change of air pressure2 seconds after box begins to fall.

Solution Summary: The author calculates the rate of change of air pressure at a height of s meters above sea level.