quadratic functions: maximum height of fireworks

[Princezz3286]

The fire department launches fireworks at an angle of 50degrees from the horizontal. The height, h, of one particular type of display can be approximated by the following function:

h(t) = ?16t^2 + 126 square root 3 t

where h is measured in feet and t is measured in seconds. Find the maximum height the fireworks will reach.

 

[Loren]

Re: quadratic functions

\(\displaystyle h(t) = -16t^2 + 126\sqrt{3}\cdot t\)

Find the derivative h' then set it equal to zero and solve for t.

\(\displaystyle h' = -32t + 126\sqrt{3}=0\)

When you find the value of t, which is the number of seconds after launch that it will reach the max, plug that back into the original equation to determine the height.

I get in the neighborhood of 740-750 ft. You can come up with the exact measure.

 

[skeeter]

if you're not into calculus yet, you can find the t-value for the vertex of the height vs. time graph using the equation \(\displaystyle t = \frac{-b}{2a}\) which will be the time the object reaches its maximum height ... once you've found that time, determine h(t) for that time to get the max height.