Studdy AI Logo
Math

QuestionCalculate the wind chill WW for t=10∘Ct=10^{\circ}C and v=1 m/sv=1 \text{ m/s} using the given formula. Round to the nearest degree.

Studdy Solution

STEP 1

Assumptions1. The wind chill factor formula is given asW={33−(10.45+10v−v)(33−t)22.030≤v<1.7733−1.5957(33−t)v>20W=\left\{\begin{array}{ll} 33-\frac{(10.45+10 \sqrt{v}-v)(33-t)}{22.03} &0 \leq v<1.77 \\ 33-1.5957(33-t) & v>20\end{array}\right. . The air temperature tt is 10∘C10^{\circ} \mathrm{C}.
3. The wind speed vv is 1 m/sec1 \mathrm{~m} / \mathrm{sec}.

STEP 2

Since the wind speed vv is 1 m/sec1 \mathrm{~m} / \mathrm{sec}, which is in the range 0≤v<1.770 \leq v<1.77, we use the first part of the formula to calculate the wind chill factor.
W=33−(10.45+10v−v)(33−t)22.03W =33-\frac{(10.45+10 \sqrt{v}-v)(33-t)}{22.03}

STEP 3

Now, plug in the given values for tt and vv into the formula.
W=33−(10.45+101−1)(33−10)22.03W =33-\frac{(10.45+10 \sqrt{1}-1)(33-10)}{22.03}

STEP 4

implify the expression inside the square root and the parentheses.
W=33−(10.45+10−1)(23)22.03W =33-\frac{(10.45+10-1)(23)}{22.03}

STEP 5

Perform the operations inside the parentheses.
W=33−19.45×2322.03W =33-\frac{19.45 \times23}{22.03}

STEP 6

Perform the multiplication operation.
W=33−447.3522.03W =33-\frac{447.35}{22.03}

STEP 7

Perform the division operation.
W=33−20.32W =33-20.32

STEP 8

Subtract to find the value of WW.
W=12.68W =12.68

STEP 9

Since we need to round to the nearest degree, we round 12.6812.68 to 1313.
W≈13∘CW \approx13^{\circ} \mathrm{C} The wind chill for an air temperature of ∘C^{\circ} \mathrm{C} and a wind speed of  m/sec \mathrm{~m} / \mathrm{sec} is approximately 13∘C13^{\circ} \mathrm{C}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord