Question

your friend rows a canoe across a river 44.0 m wide. using the gps on her phone, she determines that her total displacement is 66.0 m. how far down the river did the current move her canoe?

Explanation:

Step1: Identify the problem as a right - triangle problem

The width of the river forms one side ($a = 44.0$ m) of a right - triangle, the displacement of the canoe is the hypotenuse ($c=66.0$ m), and the distance the current moves the canoe is the other side ($b$). We use the Pythagorean theorem $c^{2}=a^{2}+b^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

$b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the given values

$b = \sqrt{(66.0)^{2}-(44.0)^{2}}=\sqrt{(66.0 + 44.0)(66.0 - 44.0)}=\sqrt{110\times22}=\sqrt{2420}\approx49.2$ m.

Answer:

$49.2$ m