Question

An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=600−16t2. Express t as a function of height h, and find the time to reach a height of 250 feet.

Answer 1

The function t(h) is t(h) =
`\sqrt{(600-h)/(16)}`

The time to reach a height 250 feet is 4.68 seconds

Explanation:

* Lets explain how to solve this problem

- An object dropped from a height of 600 feet has a height, h(t), in feet

after t seconds have elapsed, such that

h(t) = 600 − 16 t²

- We need to express t is a function of the height h

- To do that lets find t in terms of h

∵ h = 600 - 16 t²

- Add 16 t² to both sides

∴ 16 t² + h = 600

- Subtract h from both sides

∴ 16 t² = 600 - h

- Divide both sides by 16

∴ t² =
`(600-h)/(16)`

- Take √ for both sides

∴ t =
`\sqrt{(600-h)/(16)}`

∴ t(h) =
`\sqrt{(600-h)/(16)}`

* The function t(h) is t(h) =
`\sqrt{(600-h)/(16)}`

- Now lets find the time of the object to reach a height 250 feet

∵ t(h) =
`\sqrt{(600-h)/(16)}`

∵ h = 250

∴ t(250) =
`\sqrt{(600-250)/(16)}`

∴ t(250) = 4.68 seconds

* The time to reach a height 250 feet is 4.68 seconds