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Sagot :
Using the information given and linear function concepts, it is found that:
- a) The equation is: [tex]y(t) = -25t + 5000[/tex].
- b) The skydiver’s altitude after the parachute has been open for 2 minutes is of 2000 feet.
- c) It takes 200 seconds for the skydiver to reach the ground.
What is a linear function?
A linear function is modeled by:
[tex]y(t) = mt + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when t changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
Item a:
- The skydiver descends at a rate of 25 feet per second, hence [tex]m = -25[/tex].
Then:
[tex]y(t) = -25t + b[/tex]
90 seconds after the parachute opens, his altitude is 2750 feet, which means that when [tex]t = 90, y = 2750[/tex], which is used to find b. Then:
[tex]2750 = -25(90) + b[/tex]
[tex]b = 5000[/tex]
Hence, the equation is:
[tex]y(t) = -25t + 5000[/tex].
Item b:
Time is in seconds, hence, this is y(120).
[tex]y(120) = -25(120) + 5000 = 2000[/tex]
The skydiver’s altitude after the parachute has been open for 2 minutes is of 2000 feet.
Item c:
The time it takes to reach the ground is t for which y(t) = 0, hence:
[tex]-25t + 5000 = 0[/tex]
[tex]25t = 5000[/tex]
[tex]t = \frac{5000}{25}[/tex]
[tex]t = 200[/tex]
It takes 200 seconds for the skydiver to reach the ground.
You can learn more about linear functions at https://brainly.com/question/26065573
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