SOLUTION: An object's height, in meters, when thrown vertically from the ground at a velocity of 80m/s is given by the equation H=-4.9t^2+80t. Ignoring wind resistance, how many seconds will

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An object's height, in meters, when thrown vertically from the ground at a velocity of 80m/s is given by the equation H=-4.9t^2+80t. Ignoring wind resistance, how many seconds will      Log On


   

Question 724451: An object's height, in meters, when thrown vertically from the ground at a velocity of 80m/s is given by the equation H=-4.9t^2+80t. Ignoring wind resistance, how many seconds will it take the object to return to the ground? in other words, when is H=0?
In this problem, I set the equation equal to 0 then I used the quadratic formula but that was wrong....HELP PLEASE!!!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If you use the formula correctly then you can't get the wrong answer.

0+=+-4.9t%5E2+%2B+80t
a = -4.9
b = 80
c = 0
t+=+%28-%2880%29%2B-sqrt%28%2880%29%5E2-4%28-4.9%29%280%29%29%29%2F2%28-4.9%29
t+=+%28-%2880%29%2B-sqrt%286400-4%28-4.9%29%280%29%29%29%2F2%28-4.9%29
t+=+%28-%2880%29%2B-sqrt%286400-0%29%29%2F2%28-4.9%29
t+=+%28-%2880%29%2B-sqrt%286400%29%29%2F2%28-4.9%29
t+=+%28-%2880%29%2B-80%29%2F2%28-4.9%29
t+=+%28-80+%2B-+80%29%2F%28-9.8%29
which is short for:
t+=+%28-80+%2B+80%29%2F%28-9.8%29 or t+=+%28-80+-+80%29%2F%28-9.8%29
t+=+0%2F%28-9.8%29 or t+=+%28-160%29%2F%28-9.8%29
t+=+0 or t+=+800%2F49 (or approximately 16.326530612244897959183673469388)
The answer of zero reflects the fact that the object started on the ground. The other answer is the one you are looking for.

Of course this problem did not need the quadratic formula. The right side of
0+=+-4.9t%5E2+%2B+80t
factors!
0+=+t%28-4.9t+%2B+80%29
From the Zero Product Property:
t = 0 or -4.9t + 80 = 0
Solving the second one:
t = 0 or t = 800/49

It's much easier to solve these if you can factor them. The formula is complicated and mistakes can easily be made. (You must have made a mistake yourself if you didn't get the right answer.)