Question

a soccer ball is kicked 6 m north. then a teammate kicks it 3 m east into the goal. what is the soccer balls displacement from where it was first kicked?
hint: you will use pythag theorem
(1 point)
9 m northeast
3 m northeast
-3 m northeast
6.7 m northeast

Explanation:

Step1: Identify right - triangle sides

The north - ward kick of 6 m and the east - ward kick of 3 m form the two legs of a right - triangle. Let \(a = 6\) m and \(b=3\) m.

Step2: Apply Pythagorean theorem

The displacement \(d\) is the hypotenuse of the right - triangle. According to the Pythagorean theorem \(d=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 6\) and \(b = 3\) into the formula: \(d=\sqrt{6^{2}+3^{2}}=\sqrt{36 + 9}=\sqrt{45}\approx6.7\) m. The direction is northeast.

Answer:

D. 6.7 m Northeast