Question

10 anja is driving west in a straight line. after driving for 5.50 km, she turns south, and drives for 9.20 km. at the end of her drive, what is the magnitude of her displacement? 10.7 km 11.9 km 14.7 km 3.83 km

Explanation:

Step1: Apply Pythagorean theorem

The displacement \(d\) forms the hypotenuse of a right - triangle, where the two legs are \(a = 5.50\) km (west - east direction) and \(b=9.20\) km (north - south direction). The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 5.50\) and \(b = 9.20\) into the formula: \(d=\sqrt{(5.50)^{2}+(9.20)^{2}}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\((5.50)^{2}=5.50\times5.50 = 30.25\) and \((9.20)^{2}=9.20\times9.20=84.64\).
Then \(a^{2}+b^{2}=30.25 + 84.64=114.89\).

Step3: Calculate the square root

\(d=\sqrt{114.89}\approx10.7\) km.

Answer:

10.7 km