To represent the situation of two students testing their parachute designs for an egg drop project, we can define variables, relationships, and set up a system of equations based on the information provided.
Let's define:
- \( t \) = time in seconds
- \( y \) = height of the egg in feet
For the first student:
- The egg falls at a rate of 5 ft per second. Therefore, the height of the egg can be expressed as: \[ y = 10 - 5t \]
For the second student:
- The egg falls at a rate of 3 ft per second. Similarly, the height of the egg can be expressed as: \[ y = 10 - 3t \]
Now we have our two equations:
- First student's design: \[ y = 10 - 5t \]
- Second student's design: \[ y = 10 - 3t \]
This system of equations represents the heights of the eggs for the two different designs as functions of time. The first equation models the egg's height over time for the design with a descent rate of 5 ft/s, while the second equation models the same for the design with a descent rate of 3 ft/s.
This system can be analyzed further to determine the time at which the eggs reach the ground (when \(y = 0\)). For each design:
- For the first design: \[ 0 = 10 - 5t \implies t = 2 \text{ seconds} \]
- For the second design: \[ 0 = 10 - 3t \implies t \approx 3.33 \text{ seconds} \]
This means the first egg will hit the ground in 2 seconds, while the second egg will hit the ground in approximately 3.33 seconds.
1 answer