# A boat is trying to cross a river that is flowing at 2 m/s. The boat can travel at 4m/s. What is the resultant velocity of the boat?

Dec 29, 2015

The resultant velocity is $2 \sqrt{5}$ m/s

#### Explanation:

On the image, we have 3 lines: the red one, that shows the boat velocity; the blue one, that shows the river velocity; and the gray one, that shows the resultant velocity. The origin is the boat.
If we change the place of the red line to the end of the blue one, as it is in the second image, we will create a triangle rectangle.
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The triangle rectangle has sides sizing 2 and 4, so, in order to find the third side(the resultant), we apply Pythagoras' formula:
${h}^{2} = {2}^{2} + {4}^{2}$
$h = \sqrt{20} = 2 \sqrt{5}$
So, the resultant of the velocities is $2 \sqrt{5}$ meters/second