Question

8 cory is driving west in a straight line. after driving for 1.7 kilometers, he turns north and drives for 4.3 km. at the end of his drive, what is the magnitude of his displacement vector? 4.6 km 5.1 km 6.0 km 3.4 km

Explanation:

Step1: Apply Pythagorean theorem

The displacement \(d\) forms the hypotenuse of a right - triangle, where the two legs are \(a = 1.7\) km (west - east component) and \(b=4.3\) km (north - south component). The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 1.7\) and \(b = 4.3\) into the formula: \(d=\sqrt{(1.7)^{2}+(4.3)^{2}}\).

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

\((1.7)^{2}=1.7\times1.7 = 2.89\) and \((4.3)^{2}=4.3\times4.3=18.49\).
Then \(a^{2}+b^{2}=2.89 + 18.49=21.38\).

Step3: Calculate the square root

\(d=\sqrt{21.38}\approx4.6\) km.

Answer:

A. \(4.6\) km