Answer:
The function t(h) is t(h) = [tex]\sqrt{\frac{600-h}{16}}[/tex]
The time to reach a height 250 feet is 4.68 seconds
Step-by-step 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 = [tex]\frac{600-h}{16}[/tex]
- Take √ for both sides
∴ t = [tex]\sqrt{\frac{600-h}{16}}[/tex]
∴ t(h) = [tex]\sqrt{\frac{600-h}{16}}[/tex]
* The function t(h) is t(h) = [tex]\sqrt{\frac{600-h}{16}}[/tex]
- Now lets find the time of the object to reach a height 250 feet
∵ t(h) = [tex]\sqrt{\frac{600-h}{16}}[/tex]
∵ h = 250
∴ t(250) = [tex]\sqrt{\frac{600-250}{16}}[/tex]
∴ t(250) = 4.68 seconds
* The time to reach a height 250 feet is 4.68 seconds
