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Once his parachute is open, a skydiver descends at a rate of 25 feet per second. 90 seconds after the parachute opens, his altitude is 2750 feet. a) Determine an equation to model the skydiver’s altitude (A) after his parachute has been open for t seconds. b) Use your equation to determine the skydiver’s altitude after the parachute has been open for 2 minutes. c) Once the parachute is open, how long does the skydiver take to reach the ground?

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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