Question

a snowflake gets blown sideways 5 ft for every 5 ft it falls downward. in one such movement, what is the total distance the snowflake travels and in what direction?

Explanation:

Step1: Identify the components of movement

The snow - flake has a vertical movement of 5 ft and a horizontal movement of 5 ft.

Step2: Use the Pythagorean theorem

The total distance \(d\) of the snow - flake's movement forms the hypotenuse of a right - triangle with legs \(a = 5\) ft and \(b = 5\) ft. The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 5\) and \(b = 5\) into the formula: \(d=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}\approx7.07\) ft.
The direction of movement can be found using trigonometry. Let \(\theta\) be the angle of the path of the snow - flake with the vertical. \(\tan\theta=\frac{5}{5}=1\), so \(\theta = 45^{\circ}\) from the vertical (towards the side - ways direction).

Answer:

The total distance the snowflake travels is \(5\sqrt{2}\approx7.07\) ft and the direction is \(45^{\circ}\) from the vertical (sideways).