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