Chapter 5.1, Problem 6PP

To determine

The distance covered in east direction .

Answer to Problem 6PP

The distance travelled in east direction is $\text{6}\text{.0 km}$.

Explanation of Solution

Given:

There is a walk of 8.0 km north and then a particular distance in due east so that the displacement between the start and end point is 10.0 km.

Formula Used:

For two given vectors A and B and their resultant R, the Pythagoras theorem is expressed as,

  $\text{R}=\sqrt{{\text{A}}^2+{\text{B}}^2}$

If the resultant and one vector is known then the unknown vector can be calculated as,

  $\text{B}=\sqrt{{\text{R}}^2-{\text{A}}^2}$

Calculation:

Graphically the given condition can be expressed as shown in Figure 1.

  

Figure 1

Here the distance travelled can be represented as vectors such that they are perpendicular to each other. One of the distance vectors has been given and the resultant displacement has been given.

Thus, Pythagoras theorem can be applied to evaluate the unknown distance which is the distance covered in east direction.

Applying the Pythagoras theorem for the given vectors, the distance travelled in east direction is obtained as ,

  $\begin{array}{c}\text{B}=\sqrt{{\left(10\right)}^2-{\left(8\right)}^2}\\ =6.0\text{ km}\end{array}$

Conclusion:

Thus, the distance travelled in east direction is 6 km.