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Chapter 6: Problem 68

A moving conveyor is built so that it rises 1 meter for each 3 meters of horizontal travel. (a) Draw a diagram that gives a visual representation of the problem. (b) Find the inclination of the conveyor. (c) The conveyor runs between two floors in a factory. The distance between the floors is 5 meters. Find the length of the conveyor.

Short Answer

Expert verified
The inclination of the conveyor is \( \tan^{-1}(\frac{1}{3}) \) degrees and the length of the conveyor is \( \sqrt{5^2 + 15^2} \) meters.

Step by step solution

01

Diagram Drawing

Visualize the problem as a right triangle. The horizontal travel of the conveyor represents the base of the triangle (3 meters), the rise of the conveyor represents the height of the triangle (1 meter).
02

Calculate Angle

To find the angle of inclination, use the formula: \( \text{angle} = \tan^{-1}(\frac{{\text{opposite}}}{\text{adjacent}}) \) where opposite is the rise of the conveyor (1 meter) and adjacent is the horizontal travel of the conveyor (3 meters), so, \( \text{angle} = \tan^{-1}(\frac{1}{3}) \)
03

Length Calculation

To find the length of the conveyor (hypotenuse of the triangle), use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \) where a is the distance between the floors (5 meters), b is the horizontal distance (found by scaling up the triangle so that the height is now 5 meters, the base would be 15 meters (3*5)), so, \( c = \sqrt{5^2 + 15^2} \)

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