SOLUTION: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is       Log On


   

Question 882144: Please help me solve this word problem: A disc is thrown into the air and follows a path modeled by the function h(t)=7.8+22t-5t^2, where time, t, is in seconds and height h(t) is in meters. Determine when the ball will land to the nearest hundredth.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Disc? Ball?
In any case, you know to expect the maximum point in the exact middle of the two roots of the h(t). The initial height is 7.8 meters (Do you see why?). That is for t=0. The t that you are looking for is the greatest value of t.

-5t%5E2%2B22t%2B7.8=0
-
t=%28-22%2B-+sqrt%2822%5E2-4%28-5%29%287.8%29%29%29%2F%282%2A%28-5%29%29, will give you the zeros of h.
t=%28-22%2B-+sqrt%2822%5E2%2B20%287.8%29%29%29%2F%28-10%29
t=%28-22%2B-+sqrt%289680%29%29%2F%28-10%29
9680=2^4*5*11^2
t=%28-22%2B-+4%2A11%2Asqrt%285%29%29%2F%28-2%2A5%29
t=%28-11%2B-+22%2Asqrt%285%29%29%2F%28-5%29,

%28-11-49.19%29%2F%28-5%29 or %28-11%2B49.19%29%2F%28-5%29
highlight%2812%2Asec%29 or cross%28-7.6%29,this root not needed.

The maximum height happens when highlight%28t=%2812%2B%28-7.6%29%29%2F2=highlight%282.2%29%29 seconds.