** a rock is thrown upward from the top of
a 25 foot tower with an initial upward
velocity of 100ft/sec. the height of a rock
above the ground as a function of time can
be modeled by the equation: h(t) =
- 16t? + 100t + 25. how long does it take
for the rock to fall back to the ground?

The rocket will take 6.49 seconds to fall back to the ground

Step-by-step explanation:

* Lets explain how to solve the problem

- A rock is thrown upward from the top of  a 25 foot tower with an initial

 upward  velocity of 100 ft/sec

- That means at t = 0 the height of the rock is 25 feet above the ground

- A function of time can  be modeled by the equation:

 h(t) =  - 16t² + 100t + 25, where h is the height of the rocket from the

 ground at time t

∵ h(t) = -16t² + 100t + 25

- The height of the rocket is 25 feet above the ground when it

  is thrown up

∴ h(t) = 25 at t = 0 ⇒ initial position of the rocket

- The height of the rocket when hits the ground is zero

∴ h(t) = 0 when the rocket hits the ground ⇒ final position of it

- We need to find the time that the rocket takes to fall back to

 the ground

∵ h(t) = 0

∵ h(t) = -16t² + 100t + 25

∴ -16t² + 100t + 25 = 0

- Lets solve it to find the value of t

∵ -16t² + 100t + 25 = 0

- Multiply both sides by -1 to make the coefficient of t² positive

∴ 16t² - 100t - 25 = 0

- Use your calculator to find the values of t

∴ t = 6.49 sec and t = -0.24 sec

∵ We will reject the value of t = -0.24, because time can not be

   negative value

∴ The rocket will take 6.49 seconds to fall back to the ground

24

step-by-step explanation: