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Physics / Physics: Principles with Applications 6 / Chapter 3 / Problem 54GP

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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A plumber steps out of his truck, walks 50 m east and 25 m south, and then takes an

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QUESTION:

A plumber steps out of his truck, walks 50 m east and 25 m south, and then takes an elevator 10m down into the subbasement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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QUESTION:

A plumber steps out of his truck, walks 50 m east and 25 m south, and then takes an elevator 10m down into the subbasement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

ANSWER:

Step 1 of 2

Here we have to find the plumber’s displacement from the truck according to components and we also need to find the respective angles too.

The plumber at first moved on the xy plane and then it went down through the z axis.

The position of the plumber is: $\left({50,\ -25,\ -10}\right)$ .

Here we have taken the positive directions as: north, east and vertically up.

The xy plane diagram will look like,

The angle $\alpha{}$ can be found as,

$\alpha{}={\tan{}}^{-1}\left({\frac{{D}_{y}}{{D}_{x}}}\right)$

$={\tan{}}^{-1}\left({\frac{25}{50}}\right)=26.5{6}^{0}$ .

And the distance covered can be calculated as,

${D}_{xy}=\sqrt{{{D}_{x}}^{2}+{{D}_{Y}}^{2}}$

$=\sqrt{2{5}^{2}+5{0}^{2}}$

$=55.9\ m$ .

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