I handcedrives her scooter 7 kilometers north. She stops for lunch and then drives 5 kilometers east. What was her displacement? It may help you to draw the scenarin. Almage result for compass B.6 km Nurtheast 3.66 km north 2.2 km south

## Step 1<br />The problem involves the concept of displacement in physics. Displacement is a vector quantity that refers to the shortest distance between the initial and final position of a point. It is the straight-line distance between the starting point and the ending point, along with the direction.<br /><br />## Step 2<br />In this problem, the person drives 7 kilometers north and then 5 kilometers east. This forms a right-angled triangle, where the two legs are the distances driven north and east, and the hypotenuse is the displacement.<br /><br />## Step 3<br />We can use the Pythagorean theorem to calculate the displacement. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.<br /><br />### **The Pythagorean theorem: \(c = \sqrt{a^2 + b^2}\)**<br /><br />## Step 4<br />Substitute the given values into the formula. Here, \(a = 7\) km (north) and \(b = 5\) km (east).<br /><br />### **Displacement: \(c = \sqrt{7^2 + 5^2} = \sqrt{49 + 25} = \sqrt{74}\)**<br /><br />## Step 5<br />The square root of 74 is approximately 8.6. However, the problem asks for the displacement in kilometers, not in square kilometers. Therefore, we need to take the square root of 74 to get the actual displacement.<br /><br />### **Displacement: \(c = \sqrt{74} \approx 8.6\) km**<br /><br />## Step 6<br />The direction of the displacement is northeast, as the person drives north and then east.