Chapter 5.1, Problem 1PP

To determine

Magnitude of displacement.

Answer to Problem 1PP

141 km

Explanation of Solution

Given:

Car is driven 125 due West then 65 km due South.

Formula Used:

If P and Q are two vectors which are perpendicular to each other, the resultant vector can be obtained as:

  $R=\sqrt{P^2+Q^2}$

Calculation:

It is given first car is driven 125 due west.

Let $P=125\text{ km}$

And then car is driven 65 km due south.

Let $Q=65\text{ km}$

From the vector additionprinciple ,when two vectors are perpendicular to each other,then their resultant magnitude is

  $\begin{array}{c}R=\sqrt{P^2+Q^2}\\ =\sqrt{{125}^2+{65}^2}\\ =\sqrt{19850}\\ \approx 141\text{ km}\end{array}$

Magnitude of displacement graphically:

It is given that first car is driven due west for 125 km.

Therefore,

  

Then, car is driven to 65 km sue to south.

Therefore,

  

So, the resultant displacement will be,

  

The magnitude of displacement is same by both mathematical and by graphical method.

Therefore, magnitude of displacement will be 141 km.