Question

Darlene kicks a soccer ball off the ground and in the air with an initial velocity of 34 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

17.7 feet

18.1 feet

19.3 feet

20.2 feet

Answer 1

@waterineyes : I mean, I know how to find the vertex, but like v and s being undefined I cannot find it!

Answer 2

@phi will help you here..

Answer 3

Okay... (o-o)
Thanks...

Answer 4

they want you to think harder about understanding a formula

here is the first hint

initial *velocity* of 34 feet per second.

Answer 5

So would s = 34? That is kind of what I was thinking. ;3

Answer 6

You should think, "H(t) tells me the height of the ball at time t"

at t=0 (just when the ball is kicked) what is the height of the ball ? Hopefully you can reason that it makes sense the ball is on the ground at height zero.

If you make t=0 in the formula
H(t) = -16t2 + vt + s,
you know you want H(0) (height of the ball at time zero) to be zero
-16 * 0^2 + v*0 + s= 0
that let's you find s.

Answer 7

in the formula "v" is short for the velocity of the ball.

Answer 8

Can you find what "s" is ?

Answer 9

Um.I can't seem to calculate this...

What I understand right now is that v = 34 and s might be 0?

Answer 10

And t is zero after time is 0 seconds...

Answer 11

yes. v=34 and s=0

Darlene kicks a soccer ball off the ground. (i.e. ball has height 0 at t=0 )
formula H(t) = -16t2 + vt + s
tells you the height at each time. The idea is at time t=0 the ball is kicked. At t=0 it is on the ground. If we use t=0 in the formula we find H(0)= s
but H(0) (height of the ball at t=0) is zero, so s=0

Answer 12

you should find
\[ H(t) = -16t^2 + 34t \]

Answer 13

Can you find the vertex (where the ball will be highest) ?

Answer 14

Okay, so find the vertex (maximum) of that equation. I know the way they taught me to find the vertex.

Answer 15

\[h(t)=-16t^2+34t+0\]First I find the x-coordinate...
\[t=\frac{ -b }{ 2a }=\frac{ -34 }{ 2(-16) }=\frac{ -34 }{ -32 }=-66\]Now I have to substitue the x-coordinate and solve for h(t)\[h(-66)=-16(-66)^2+34(-66)+0\]\[h(-66)=-16(-4356)+34(-66)\]\[-71940\]Now I write it as an ordered pair...
(-66, -71940)

I think this is wrong. (o-o)

Answer 16

-34/-32 is not -66

first, minus divided by minus is positive.
second 34/32 is very close to 32/32 = 1
so expect a number a little bigger than 1

Answer 17

Oops, I must have accidentally hit the minus sign. cx

Answer 18

Oh thanks! I got 18.0625. cx

sorry bout that, thanks. c;

Answer 19

Yes, and if you round to the nearest tenth, you get 18.1

Here is a plot of the parabola

Answer 20

Oh thanks! Also, I did not get how to find "How long it will take to hit the ground"

I am not going to ask a specific question, but I just need a little help on it, especially since 25% of my state exam is going to be questions like these. .-.

Answer 21

There are a few ways to answer the question.
One way:
a parabola is symmetric (see the graph)
If it takes a certain amount of time to get up to the "top" it will take the same amount of time to get back down. As long as we start at height = zero and end up at height =0, we can just double the amount of time it takes to get to the peak.

Answer 22

Another way:
the formula H(t) tells you the height of the ball at time t
If the ball starts on the ground goes up, and then hits the ground, we can set up this formula:
\[ -16t^2 +34t = 0 \]
that equation says: find all the times where the ball is on the ground (has height 0)
so solve that equation. ( I would factor out the t)