Q25E - University Physics with Modern Physics

Question

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.)

Step-by-Step Solution

Answer

The displacement is $7.8 km$ and the direction is ${38}^0$with respect to the x-axis.

Step 1: 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 

$\theta ={{\tan }^{-}}^1\left(\frac{y}{x}\right)$…………………(1)

Step 2: Finding the magnitude

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

 $\frac{4}{x}=\frac{y}{z}$

 

For x, measure the length of the $4.0 km$-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 $7.8 km$ and the direction is  $38°$ with respect to the x-axis