Chapter 5, Problem 55A

To determine

Total displacement of the car.

Answer to Problem 55A

Total displacement of the car is 79.05 km.

Explanation of Solution

Given:

Car moves first 65 km in the east direction and then 45 km in the west direction.

Formula Used:

The resultant of two vectors is given by,

  $R=\sqrt{P^2+Q^2}$

Here, P and Q are two vectors which are perpendicular to each other.

Calculation:

It is given first car displacement is 65 m due east.

Let $P=65\text{ km}$

And then 45 m due west.

Let $Q=45\text{ km}$

East and west direction is perpendicular to each other. From the vector principle when two vectors are perpendicular to each other then their resultant magnitude is given by,

  $\begin{array}{c}R=\sqrt{P^2+Q^2}\\ =\sqrt{{65}^2+{45}^2}\\ =\sqrt{6250}\\ =\text{ 79}\text{.05 km}\end{array}$

Conclusion:

Therefore, total displacement is 79.05 km.