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?

7.07 ft at 45° from straight downwards.

6.01 ft at 45° from straight downwards.

6.01 ft at 30° from straight downwards.

6.01 ft at 50° from straight downwards.

Explanation:

Step1: Recognize right - triangle situation

The snowflake's downward and sideways movements form a right - triangle with legs of length $a = 5$ ft and $b = 5$ ft.

Step2: Calculate the total distance (hypotenuse)

Use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 5$ and $b = 5$: $c=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}\approx7.07$ ft.

Step3: Calculate the direction

The tangent of the angle $\theta$ from the straight - downward direction is $\tan\theta=\frac{\text{sideways distance}}{\text{downward distance}}$. Since $\frac{5}{5}=1$, then $\theta=\arctan(1) = 45^{\circ}$.

Answer:

$7.07$ ft at $45^{\circ}$ from straight downwards.