Vector Mechanics for Engineers: Statics and Dynamics
Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259638091
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 11.1, Problem 11.5P

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)

Expert Solution
Check Mark
To determine

The maximum altitude (ymax) that the hikers reach.

Answer to Problem 11.5P

The maximum altitude (ymax) that the hikers reach is 11,980ft_.

Explanation of Solution

Given information:

The curve fit equation with function of time is y(t)=0.12t56.75t4+135t31120t2+3200t+9070.

Calculation:

Write the relation for the motion of car:

y(t)=0.12t56.75t4+135t31120t2+3200t+9070 (1).

Here, position of car is x and time is t.

Differentiate Equation (1) with respect to time.

dxdt=0.6t427t4+405t32240t2+32000=0.6t427t4+405t32240t2+3200

Solve the above equation to find the roots.

The roots values are 2.151hours, 8.606hours, 14.884hours and 19.36hours.

Calculate the hike y(2.151):

Substitute 2.151hours for t in Equation (1).

y(2.151)={0.12(2.151)56.75(2.151)4+135(2.151)31120(2.151)2+3,200(2.151)+9,070}=5.756144.499+1,343.5545,182.017+6,883.2+9,070=11,976.044ft11,976ft

Calculate the hike y(8.606):

Substitute 8.606hours for t in Equation (1).

y(8.606)={0.12(8.606)56.75(8.606)4+135(8.606)31120(8.606)2+3200(8.606)+9070}=(5,664.84437,026.1998+86,047.40882,950.824+27,539.2+9,070)=8,344.428ft8,344ft

Calculate the hike y(14.884)

Substitute 14.884hours for t in equation (1).

y(14.884)={0.12(14.884)56.75(14.884)4+135(14.884)31,120(14.884)2+3,200(14.884)+9,070}=(87,655.577331,270.237+445,136.035248,117.471+47,628.8+9,070)=10,102.704ft10,103ft

Neglect the root 19.36 because the value is greater than 18 hours.

Calculate the hike y(18) using equation (1).

Substitute 18 for t in equation (1).

y(18)={0.12(18)56.75(18)4+135(18)31,120(18)2+3,200(18)+9,070}=226,748.16708,588+787,320362,880+57,600+9,070=9,270.16ft9,270ft

Therefore, the maximum altitude (ymax) that the hikers reach is 11,976ft_.

(b)

Expert Solution
Check Mark
To determine

The total feet they ascend.

Answer to Problem 11.5P

The total feet they ascend is 4,665ft_.

Explanation of Solution

Given information:

The function of time is y(t)=0.12t56.75t4+135t31120t2+3200t+9070.

Calculation:

Calculate the hike with respective time (t) as in Table 1.

Time (t)Hike (ft)
09070
111278.4
211965.8
311717.4
410984.9
510101.3
69295.12
78705.09
88394.16
98364.13
108570
118934.37
129361.84
139753.41
1410020.9
1510101.3
169971.12
179661.09
189270.16

Plot the graph for time versus hike as in Figure (1).

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 11.1, Problem 11.5P

Calculate the hike y(0):

Substitute 0hours for t in Equation (1).

y(0)={0.12(0)56.75(0)4+135(0)31,120(0)2+3,200(0)+9,070}=00+00+3,200+9,070=9,070ft

Calculate the total feet they ascend using the relation:

Totalfeetascend=(y(2.151)y(0))+(y(14.884)y(8.606))

Substitute 9070ft for y(0), 11,976ft for y(2.151), 8,340ft for y(8.606), and 10,103ft for y(14.884).

Totalfeetascend=(11,9769,070)+(10,1038,344)=2,906+1,759=4,665ft

Therefore, the total feet they ascend is 4,665ft_.

(b)

Expert Solution
Check Mark
To determine

The total feet they descend.

Answer to Problem 11.5P

The total feet they descend is 4,469ft_.

Explanation of Solution

Given information:

The function of time is y(t)=0.12t56.75t4+135t31120t2+3200t+9070.

Calculation:

Calculate the total feet they descend using the relation:

Totalfeetascend=(y(2.151)y(8.606))+(y(14.884)y(18))

Substitute 9,270ft for y(18), 11,976ft for y(2.151), 8,340ft for y(8.606), and 10,103ft for y(14.884).

Totalfeetdescend=(11,9768,340)+(10,1039,270)=3,636+833=4,469ft

Therefore, the total feet they descend is 4,469ft_.

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Chapter 11 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 11.1 - The brakes of a car are applied, causing it to...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - Many car companies are performing research on...Ch. 11.1 - A Scotch yoke is a mechanism that transforms the...Ch. 11.1 - For the Scotch yoke mechanism shown, the...Ch. 11.1 - A piece of electronic equipment that is surrounded...Ch. 11.1 - A projectile enters a resisting medium at x = 0...Ch. 11.1 - Point A oscillates with an acceleration a =...Ch. 11.1 - A brass (nonmagnetic) block A and a steel magnet B...Ch. 11.1 - Based on experimental observations, the...Ch. 11.1 - A spring AB is attached to a support at A and to a...Ch. 11.1 - Prob. 11.21PCh. 11.1 - Starting from x = 0 with no initial velocity, a...Ch. 11.1 - A ball is dropped from a boat so that it strikes...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - A human-powered vehicle (HPV) team wants to model...Ch. 11.1 - Prob. 11.27PCh. 11.1 - Based on observations, the speed of a jogger can...Ch. 11.1 - The acceleration due to gravity at an altitude y...Ch. 11.1 - The acceleration due to gravity of a particle...Ch. 11.1 - The velocity of a particle is v = v0[1 sin(t/T)]....Ch. 11.1 - An eccentric circular cam, which serves a similar...Ch. 11.2 - An airplane begins its take-off run at A with zero...Ch. 11.2 - A minivan is tested for acceleration and braking....Ch. 11.2 - Steep safety ramps are built beside mountain...Ch. 11.2 - A group of students launches a model rocket in the...Ch. 11.2 - A small package is released from rest at A and...Ch. 11.2 - A sprinter in a 100-m race accelerates uniformly...Ch. 11.2 - Automobile A starts from O and accelerates at the...Ch. 11.2 - In a boat race, boat A is leading boat B by 50 m...Ch. 11.2 - As relay runner A enters the 65-ft-long exchange...Ch. 11.2 - Automobiles A and B are traveling in adjacent...Ch. 11.2 - Two automobiles A and B are approaching each other...Ch. 11.2 - An elevator is moving upward at a constant speed...Ch. 11.2 - Prob. 11.45PCh. 11.2 - Prob. 11.46PCh. 11.2 - The elevator E shown in the figure moves downward...Ch. 11.2 - The elevator E shown starts from rest and moves...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - In the position shown, collar B moves to the left...Ch. 11.2 - Collar A starts from rest and moves to the right...Ch. 11.2 - A farmer lifts his hay bales into the top loft of...Ch. 11.2 - The motor M reels in the cable at a constant rate...Ch. 11.2 - Collar A starts from rest at t = 0 and moves...Ch. 11.2 - Collars A and B start from rest, and collar A...Ch. 11.2 - Block B starts from rest, block A moves with a...Ch. 11.2 - Prob. 11.58PCh. 11.2 - The system shown starts from rest, and each...Ch. 11.2 - Prob. 11.60PCh. 11.3 - A particle moves in a straight line with a...Ch. 11.3 - Prob. 11.62PCh. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - Prob. 11.66PCh. 11.3 - A commuter train traveling at 40 mi/h is 3 mi from...Ch. 11.3 - Prob. 11.68PCh. 11.3 - In a water-tank test involving the launching of a...Ch. 11.3 - The acceleration record shown was obtained for a...Ch. 11.3 - Prob. 11.71PCh. 11.3 - Prob. 11.72PCh. 11.3 - Prob. 11.73PCh. 11.3 - Car A is traveling on a highway at a constant...Ch. 11.3 - Prob. 11.75PCh. 11.3 - Prob. 11.76PCh. 11.3 - Prob. 11.77PCh. 11.3 - Prob. 11.78PCh. 11.3 - An airport shuttle train travels between two...Ch. 11.3 - Prob. 11.80PCh. 11.3 - Prob. 11.81PCh. 11.3 - The acceleration record shown was obtained during...Ch. 11.3 - Prob. 11.83PCh. 11.3 - Prob. 11.84PCh. 11.3 - An elevator starts from rest and rises 40 m to its...Ch. 11.3 - Two road rally checkpoints A and B are located on...Ch. 11.3 - As shown in the figure, from t = 0 to t = 4 s, the...Ch. 11.3 - Prob. 11.88PCh. 11.4 - Two model rockets are fired simultaneously from a...Ch. 11.4 - Ball A is thrown straight up. 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