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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 1 - Problem 64pp
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 1 - Problem 64pp

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Solved: Growth Speed The images of trees in Figure P1.68 ISBN: 9780321570567 2

Solution for problem 64PP Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 64PP

Growth Speed The images of trees in Figure P1.68 come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. What is this speed in m/s?

Step-by-Step Solution:
Step 1 of 3

ANSWER: STEP 1:- Here the growth of the tree is given in units of feets for each year. In the 1 st yr (1 to 2 nd yr) the height of the tree increased by, 21 - 12 = 9 feet. In the 2 nd yr (2 to 3rd yr) the height increased by 30 - 21 =9 feet. The total growth of the tree in the years between 1 to 3 is, 9 +9 = 18 feet. The total time taken for this is 3 - 1 = 2 years So the speed will be, speed = increase in height / time taken---------------------(1) = 18 ft / 2 yrs = 9 ft/yr STEP 2:- But we need to convert it into meter per seconds. So, let’s work on it. We know that 1 ft = 0.3048 meters So, 9 ft = 9×0.3048 = 2.7432 m And we also know that, 1 yr = 365 days= 365×24 hrs = 365×24×3600 s = 31536000 s Now our job is to put the distance and time in equation (1) with the revised units. So, speed = increase in height / time taken---------------------(1) = 9 ft/yr = 2.7432 m /31536000 s 8 8 = 8.69×10 m/s = 8.7×10 m/s(approximately) CONCLUSION: 8 So the speed we got for the growth of the tree is 8.7×10 m/s.

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ISBN: 9780321570567

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