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From a fixed point on the ground, the distance to a

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 3E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

From a fixed point on the ground, the distance to a certain tree is measured to be s = 55.2 ± 0.1 m and the angle from the point to the top of the tree is measured to be θ= 0.50 ± 0.02 radians. The height of the tree is given by h = s tan θ.

a. Estimate h, and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in h: reducing the uncertainty in s to 0.05 m or reducing the uncertainty in θ to 0.01 radians?

Step-by-Step Solution:

Step 1 of 5</p>

Here we have to find the uncertainty of the height of the tree

Given height of the tree is

The distance to certain tree is measured to be S=55.20.1 m

From this S=55.2,

The angle from the point to the top of the tree is  

 From this =0.5,

Step 2 of 5</p>

a) Then    

                 h=55.2(0.5)

                   =30.16

Step 3 of 5</p>

Now differentiate h with respect to s and  

     = tan (0.5)

    =0.5463

     =(55.2) sec

    =71.674

Step 4 of 5

Chapter 3.4, Problem 3E is Solved
Step 5 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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