Question 212927
First, substitute the height of 200 feet for h in the equation:


200=0.04t^2 +2t


Since it's a quadratic equation, set it equal to zero by subtracting 200 from each side:

0=0.04t^2 + 2t -200


Next I would get rid of that ugly decimal by multiplying both sides by 100:
0= 4t^2 + 200t - 20000


Divide both sides by 4:
0=t^2 + 50t -5000


Next, to solve by factoring you must find two numbers with opposite sign whose product is 5000 (actually -5000!) and whose difference is 50 (to give you the middle term of +50t).  The first combination of numbers that came to mind for me was 50*100.  That's the one!!


0=(t+100)(t-50)

t=-100 or t=50


Reject the negative answer, since time cannot be negative, and the answer must be t=50 sec.


R^2


Dr. Robert J. Rapalje
Seminole Community College
Altamonte Springs Campus