Question 1055228: If a model rocket is launched with a trajectory of h(t) = -16t^2+96t+112 (where t = time in seconds), what is the maximum height the rocket reaches? When does it hit the ground?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If a model rocket is launched with a trajectory of h(t) = -16t^2+96t+112 (where t = time in seconds),
what is the maximum height the rocket reaches? When does it hit the ground?
-----
Height is zero when the rocket hits the ground.
-----
-16t^2 + 96t + 112 = 0
--------------------------
t^2 - 6t - 7 = 0
-----
(t-7)(t+1) = 0
-----
The rocket hits the ground at t = 7 seconds
---------------------
The max height occurs when t = -b/(2a) = -96/((-2)*16) = 3 sec
---
That max height = f(3) = -16*3^2 + 96*3 + 112 = 256 ft
-----------------
Cheers,
Stan H
---------------
|
|
|
