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A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.)

Short Answer

Expert verified

The displacement is 7.8kmand the direction is 380with respect to the x-axis.

Step by step solution

01

The vector and its direction

The vector's various coordinates are presented here. We know that in coordinates, the x component of a vector comes first, followed by the y component. To calculate the angle of the vector with respect to the x-axis, just multiply the y component by the x component and then take the inverse of that result.

This will tell you the vector's angle with the x-axis.

It can be represented as


=tan-1(yx)鈥︹赌︹赌︹赌︹赌︹赌︹赌(1)

02

Finding the magnitude

Use a ruler to determine the magnitude of the displacement vector along with the following formula.

4x=yz

For x, measure the length of the 4.0km-vector and plug it in. Measure the length of the displacement vector for z and plug it in. Then, given y, the magnitude, solve the equation. Determine the angle above the horizontal with a protractor.

Measurement of final displacement

Hence the displacement is 7.8kmand the direction is 38with respect to the x-axis

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