Explanation Given information: A moving van with a gross weight of 8000 pounds is parked on a street with a 5 0 grade. Explanation: The total force ( F ) required to keep the van from rolling down the hill is splits into two components one is going down and other is perpendicular to the hill. Let F d be the component of force going down, F p be the component of force perpendicular to the hill To draw a force diagram using vectors as shown in below figure. In Δ A B C and Δ B D E , ∠ C = ∠ E since both are right angles. Sides A B and B D are parallel sides so the alternating angles ∠ A B C = ∠ B D E The sides in front of equal angle are same so A B = B E Thus, Δ A B C ∼ Δ B D E . So ∠ B A C = ∠ D B E = 5 0 , A B = B D = F , A C = B E = F p and B C = D E = F d A moving van with a gross weight of 8000 pounds so ‖ F ‖ = 8000 To find magnitude of F d , In Δ A B C use trigonometric ratio, sin 5

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter 8, Problem 62RE

To determine

The magnitude of the force required to keep the van from rolling down the hill and the magnitude of the force perpendicular to hill where a moving van with a gross weight of 8000 pounds is parked on a street with a 50 grade.

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Chapter 8, Problem 61RE

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Chapter 8 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Ch. 8.1 - Prob. 1AYU Ch. 8.1 - Prob. 2AYU Ch. 8.1 - Prob. 3AYU Ch. 8.1 - Prob. 4AYU Ch. 8.1 - Prob. 5AYU Ch. 8.1 - Prob. 6AYU Ch. 8.1 - Prob. 7AYU Ch. 8.1 - Prob. 8AYU Ch. 8.1 - Prob. 9AYU Ch. 8.1 - Prob. 10AYU

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The magnitude of the force required to keep the van from rolling down the hill and the magnitude of the force perpendicular to hill where a moving van with a gross weight of 8000 pounds is parked on a street with a 5 0 grade.

Solution Summary: The author explains how the force required to keep the van from rolling down the hill is divided into two components.

The magnitude of the force required to keep the van from rolling down the hill and the magnitude of the force perpendicular to hill where a moving van with a gross weight of 8000 pounds is parked on a street with a 50 grade.

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Chapter 8 Solutions