If the path of a diver diving from a diving board is given by the model: h = - 0.44t2 + 2.2t + 10 where the h represents the height of the diver at t seconds after she leaves the board. Find the time (in seconds) that it takes for her to reach the maximum height for the dive.

Question

If the path of a diver diving from a diving board is given by the model: h = - 0.44t2 + 2.2t + 10 where the h represents the height of the diver at t seconds after she leaves the board.   Find the time (in seconds) that it takes for her to reach the maximum height for the dive.

anonymous · Answer

0.88 sec

kropot72 · Answer

Differentiate h with respect to t as a first step. Can you do this?

anonymous · Answer

yes

kropot72 · Answer

Good. What do you get for dh/dt?

anonymous · Answer

nevermind i have no clue

kropot72 · Answer

$$\frac{dh}{dt}=-0.88t+2.2$$
If the derivative is put equal to zero we can solve to find t for the maximum height.
-0.88t + 2.2 = 0
0.88t = 2.2
t = 2.2/0.88 = 2.5 seconds

anonymous · Answer

differentiate???

anonymous · Answer

thanks

kropot72 · Answer

You're welcome :)

anonymous · Answer

heck no
max is at $-\frac{b}{2a}=-\frac{2.2}{2\times -.44}=2.5$

anonymous · Answer

i am going to bet ( i could certainly be mistaken) that @tbrooks3  is not taking a calc class for this. maybe i am wrong

anonymous · Answer

this is a algebra 1 class at my school

anonymous · Answer

that is what i thought. 
so "derivative" makes no sense to you right?

anonymous · Answer

right.. ive been told that soo many times today but had no clue

kropot72 · Answer

Why did @tbrooks3 answer yes to "Can you do this?" Never mind.

anonymous · Answer

i had read something similar thru my class and got confused @kropot72

anonymous · Answer

that is what i thought.
if you have something that looks like 
$$y=ax^2+bx+c$$ or 
$$h=at^2+bt+c$$ then max or min occurs at vertex, which you find by computing $-\frac{b}{2a}$

kropot72 · Answer

@satellite73 Point taken. Thank you for guidance :)