Quadratic Formula

#10 - Roots of a Quadratic Equation

As I sat on the plane, ready to take off, I watched the strong October winds blow the leaves of the trees. For many months, I looked forward to boarding the plane to Seattle, as it marked the real start of my foreign exchange journey to the United States from Germany. As the plane launched into the air, my stomach began to turn. Soon, the pilot came over the speakers to say that the wind speed was relatively high at 20 mph, but he had 20 years of flying experience so we need not worry. Throughout the trip, we faced quite a bit of turbulence, which scared me at first. Once we landed, I wondered if the 11 hour flight would have been shorter if the plane was flying in the same direction as the wind. According to SciJinks¹, I would be flying against the wind on the way to Seattle and in the direction of the wind on the way home. I wanted to know what to anticipate for my trip home, so I decided to do the math.

Adding the 20 mph winds, the equations will be:

x - 20 = y for the flight to Seattle, flying against the wind

x + 20 = y for the flight back to Frankfurt, flying with the wind

To calculate the time, we are using this formula:

t = time, d = distance, s = speed

With the distance between Frankfurt and Seattle being 5080 miles, we can substitute the variables.

Now we will get rid of the fractions by multiplying by (x - 20) and (x + 20).

A quadratic equation! We can use the formula for roots of a quadratic equation.

Since there is no such thing as negative speed, the plane traveled 463 miles per hour on average. This made me think about what allows the plane to go at the speed that they do. I remembered learning about how much carbon is emitted by planes as a result of their powerful engines. I felt this was important to include because although I rarely fly, I know it is important to understand the impact that my choice has on the planet. 92kg of CO2 is emitted per hour² of a flight on a Boeing 747-400, which are used for long distance international flights. This means the 22 hours of air travel would result in 2024kg CO2 emission. I now wonder if the plane would use less fuel if the wind was propelling it forward in addition to the engine! I plan to calculate this on my flight home. Understanding what it took to get me to Seattle helps me look forward to my trip home.

References

¹What Are Trade Winds? | NOAA SciJinks – All About Weather. (n.d.). Home | NOAA SciJinks – All About Weather. Retrieved February 22, 2022, from https://scijinks.gov/trade-winds/

²Aviation. (n.d.). Carbon Footprint Calculator. Retrieved February 22, 2022, from https://www.carbonindependent.org/22.html