Question

1. a dog runs 2 miles south and then 5 miles west. what is the dogs displacement? 5.39 miles southwest 6 miles southwest 4.5 miles southwest 6.39 miles southwest

Explanation:

Step1: Apply Pythagorean theorem

The displacement \(d\) is the hypotenuse of a right - triangle with legs \(a = 2\) miles (south) and \(b=5\) miles (west). The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 2\) and \(b = 5\) into the formula: \(d=\sqrt{2^{2}+5^{2}}=\sqrt{4 + 25}=\sqrt{29}\).

Step2: Calculate the value of \(\sqrt{29}\)

\(\sqrt{29}\approx5.39\) (using a calculator, \(\sqrt{29}\approx5.385\approx5.39\)).

Answer:

5.39 miles southwest