Question

Jake tosses a coin up in the air and lets it fall on the ground. The equation that
models the height (in feet) and time in seconds) of the parabola is
- -16t2 + 24 + 6. When does the coin reach its greatest height?

Answer 1

Answer:

The coin will reach the maximum height of 15 feet in $\frac{3}{4}$ second

Step-by-step explanation:

The equation that models the height (in feet) and time in seconds) of the parabola is

$h(t)=-16t^2 + 24t + 6$

The coin will reach its greatest height at the parabola's vertex. Find the coordinates of the vertex.

From the function expression:

$a=-16\\ \\b=24\\ \\c=6$

Now,

$t_v=\dfrac{-b}{2a}\\ \\=-\dfrac{24}{2\cdot (-16)}\\ \\=\dfrac{24}{32}\\ \\=\dfrac{3}{4}\ second$

Then

$h_v=h(t_v)\\ \\=-16\cdot \left(\dfrac{3}{4}\right)^2+24\cdot \dfrac{3}{4}+6\\ \\=-16\cdot \dfrac{9}{16}+18+6\\ \\=-9+24\\ \\=15\ feet$