Concept explainers
A group of hikers uses a GPS while doing a 40-mile trek in Colorado. A curve fit to the data shows that their altitude can be approximated by the function y(t) = 0.12t5 − 6.75t4 + 135t3 − 1120t2 + 3200t + 9070, where y and t are expressed in feet and hours, respectively. During the 18-hour hike, determine (a) the maximum altitude that the hikers reach, (b) the total feet they ascend, (c) the total feet they descend. Hint: You will need to use a calculator or computer to solve for the roots of a fourth-order polynomial.
(a)
The maximum altitude
Answer to Problem 11.5P
The maximum altitude
Explanation of Solution
Given information:
The curve fit equation with function of time is
Calculation:
Write the relation for the motion of car:
Here, position of car is x and time is t.
Differentiate Equation (1) with respect to time.
Solve the above equation to find the roots.
The roots values are
Calculate the hike
Substitute
Calculate the hike
Substitute
Calculate the hike
Substitute
Neglect the root 19.36 because the value is greater than 18 hours.
Calculate the hike
Substitute
Therefore, the maximum altitude
(b)
The total feet they ascend.
Answer to Problem 11.5P
The total feet they ascend is
Explanation of Solution
Given information:
The function of time is
Calculation:
Calculate the hike with respective time (t) as in Table 1.
Time (t) | Hike (ft) |
0 | 9070 |
1 | 11278.4 |
2 | 11965.8 |
3 | 11717.4 |
4 | 10984.9 |
5 | 10101.3 |
6 | 9295.12 |
7 | 8705.09 |
8 | 8394.16 |
9 | 8364.13 |
10 | 8570 |
11 | 8934.37 |
12 | 9361.84 |
13 | 9753.41 |
14 | 10020.9 |
15 | 10101.3 |
16 | 9971.12 |
17 | 9661.09 |
18 | 9270.16 |
Plot the graph for time versus hike as in Figure (1).
Calculate the hike
Substitute
Calculate the total feet they ascend using the relation:
Substitute
Therefore, the total feet they ascend is
(b)
The total feet they descend.
Answer to Problem 11.5P
The total feet they descend is
Explanation of Solution
Given information:
The function of time is
Calculation:
Calculate the total feet they descend using the relation:
Substitute
Therefore, the total feet they descend is
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics