Question

1. a hiker follows a trail for 9 miles north, then turns and hikes 3 miles west. determine the hikers displacement.

6 miles northwest
9 miles northwest
9.49 miles northwest
12 miles north

Explanation:

Step1: Recognize the displacement as the hypotenuse of a right - triangle

The hiker's path forms a right - triangle. One leg \(a = 9\) miles (north) and the other leg \(b=3\) miles (west). The displacement \(d\) is the length of the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 9\) and \(b = 3\) into the formula: \(d=\sqrt{9^{2}+3^{2}}=\sqrt{81 + 9}=\sqrt{90}\approx9.49\) miles. The direction is northwest (since the hiker moved north and then west).

Answer:

C. 9.49 miles northwest