# EWEEK 2021: SYSTEMS ENGINEERING

Date of the Problem
February 23, 2021
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### Solve Tuesday's Problem

Systems engineers work in many different engineering fields. They need expertise in both breadth and depth, often serving as both project manager and chief engineer. While more specialized engineers work on individual sub-systems and components of a large project, the systems engineer is needed to make sure they all work together to perform the overall desired function of the product.

Kami is a systems engineer at a car manufacturer. Her team has been tasked with creating “a family sedan that rides like a sports car.” She has been working closely with the engineers designing the different components that all play a part in a car’s functioning, but she needs to test and improve the sedan’s aerodynamic efficiency to ensure their design will be aerodynamic enough to feel as fast as a sports car to consumers.

2.1) One measurement that contributes to a car’s aerodynamic efficiency is its coefficient of drag (Cd), which refers to the resistance of the car as it travels through the air. Typical sedans have a coefficient of drag between 0.34 and 0.50, but to meet the project goal of “a family sedan that rides like a sports car,” the Cd of the team’s sedan must be comparable to a typical sports car.

Based on the table below showing the Cd of the 11 most popular sports car models, what is the median Cd of a typical sports car?

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2.2) The other measurement that contributes to a car’s aerodynamic efficiency is its frontal area (A), or the total amount of space the car occupies when it is viewed from the front. This is calculated as 85% of height × width. The team’s first design, Sedan A, is shown below. To the nearest thousandth, what is the frontal area of Sedan A?

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2.3) To compare the aerodynamics of two cars, engineers compare the value of the product of the coefficient of drag and the frontal area, or CdA. The lower the value of CdA, the faster the car. Kami asks her team for two more designs, Sedan B and Sedan C. All three designs have a Cd equal to what you calculated in 2.1. Which design should Kami choose if she wants the fastest sedan—Sedan A, Sedan B or Sedan C?

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Math topic
CCSS (Common Core State Standard)
Difficulty