Question

Derek kicks a soccer ball off the ground and in the air with an initial velocity of 31 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

A)14.2 feet
B)14.6 feet
C)15.0 feet
D)15.3 feet


I am clueless on how to do this! Please help!

Answer 1

What level of math are you in?

Answer 2

@Vandreigan Algebra 1

Answer 3

Well, there are multiple ways to do this. Without using calculus, we need to find the vertex of the parabola represented by your given function.

The vertex occurs at a time t where:

\[t = \frac{-b}{2a}\]

Find this t, and then plug it back into the original equation. This will give the height of the vertex. Since this parabola is "opening downward," this is the maximum height reached.

Answer 4

i dont know the value of 'b' is but i think 'a' is -16 right?

Answer 5

b is your "v" in this one. 31 as you have typed it.

Answer 6

ohhh okay. so the axis of symmetry is .96875 which is 0.97 rounded to the nearest hundredth...?

Answer 7

Right. It's symmetric around t = 0.96875, which also tells us that this is where we find the vertex of the parabola (which is the highest/lowest point of the parabola, depending on the direction of opening)

Answer 8

ok and we already know that itll be the max point... so now its
H(.97)=-16(.97)^2+31(.97)+s which i think 2 is = 0 but im not sure

Answer 9

They should tell you what s equals. Without the s, I get 15.015625.

That is, my final answer, with the information that I have, is 15.015625+s

But yeah, you just evaluate what you are given.

Answer 10

If the ground is completely level, s = 0 (s is your initial height)

Answer 11

Yeah it is from the ground so they want you to assume the it is equal to 0, so that should be the right answer, which is C. Thank you soooo so much you've helped me a lot!

Answer 12

My pleasure :)