SOLUTION: A water ballon is launched from a launcher, up into the air from a platform. The height of the balloon in feet, is a function of the time in seconds since it was launched: f(t)= 16

Algebra ->  Functions -> SOLUTION: A water ballon is launched from a launcher, up into the air from a platform. The height of the balloon in feet, is a function of the time in seconds since it was launched: f(t)= 16      Log On


   

Question 1015369: A water ballon is launched from a launcher, up into the air from a platform. The height of the balloon in feet, is a function of the time in seconds since it was launched: f(t)= 16t^2+V0t+H0 where V0 represents the initial upward velocity of the launch, and H0 represents the height of balloon right when it is launched. Lorenzo launches his water balloon with an initial upward velocity of 80 ft per second. The initial height of the water balloon is 5ft off the ground what is the maximum height of the water balloon?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You are missing a minus sign in front of the 16t%5E2 .
system%28f%28t%29=-16t%5E2%2BV%5B0%5Dt%2BH%5B0%5D%2CV%5B0%5D=80%2CH%5B0%5D=5%29--->f%28t%29=-16t%5E2%2B80t%2B5

JUST USING ALGEBRA:
.

APPLYING A FORMULA:
f%28t%29=-16t%5E2%2B80t%2B5 is a quadratic function.
A quadratic function f%28x%29=ax%5E2%2Bbx%2Bc with a%3C0 has a maximum at x=%28-b%29%2F2a ,
so, in this case, with system%28x=t%2Ca=-16%2Cb=80%2Cc=5%29 ,
the maximum happens at t=%28-80%29%2F%282%28-16%29%29=%28-80%29%2F%28-32%29=2.5 .
The maximum is f%282.5%29=-16%2A2.5%5E2%2B80%2A2.5%2B5=-16%2A6.25%2B200%2B5-100%2B200%2B5=105

So, the maximum height of the water balloon is highlight%28105feet%29 .