SOLUTION: The equation h=-16t^2+80t models the height h feet reached in t seconds by an object propelled straight up from the ground. How long will the object be in the air until it hits the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The equation h=-16t^2+80t models the height h feet reached in t seconds by an object propelled straight up from the ground. How long will the object be in the air until it hits the      Log On


   

Question 404845: The equation h=-16t^2+80t models the height h feet reached in t seconds by an object propelled straight up from the ground. How long will the object be in the air until it hits the ground?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
h=-16t%5E2%2B80t
The key for this problem is recognizing that if the object is back on the ground, then its height, h, would be zero. So if we replace the h with zero, then we can solve for the time, t:
0=-16t%5E2%2B80t
The easiest way to solve this is by factoring. This factors quite easily:
0=16t%28-t%2B5%29
From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So:
16t = 0 or -t+5 = 0
Solving these we get:
t = 0 or t = 5
The t=0 solution represents the fact that at the start, just before being propelled into the air, the object is on the ground. The t=5 time represents the time when the object returns to the ground. So the answer to your problem is:
The object will return to the ground after 5 seconds.