# Thread: Height of a ball Word Problem!

1. ## Height of a ball Word Problem!

Hello everyone,

I'm stuck on this problem and would love an explanation:

If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
S=100+64t-16t(squared), where S is in feet and t is in seconds.

Find the max height the ball will reach??

Thanks

2. Originally Posted by Annb

If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
S=100+64t-16t(squared), where S is in feet and t is in seconds.

Find the max height the ball will reach??
the graph formed by $\displaystyle s(t) = 100+64t-16t^2$ is an inverted parabola ... the ball reaches its maximum height at the vertex of that parabola.

does the expression $\displaystyle \frac{-b}{2a}$ ring a bell ?

3. Originally Posted by Annb
Hello everyone,

I'm stuck on this problem and would love an explanation:

If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
S=100+64t-16t(squared), where S is in feet and t is in seconds.

Find the max height the ball will reach??

Thanks
Well, this - $\displaystyle s(t)=100+64t-16t^2$ - is simply a parabola that opens downward. Do you know how to find the vertex?

4. no : (

5. Originally Posted by Annb
no : (
You may need a refresher. Check out these links:

Vertex of a Parabola

The Vertex of a Parabola

6. is it y=ax squared + bx + c?

7. Originally Posted by Annb
is it y=ax squared + bx + c?
Yes, that is the standard equation of a parabola.

So, in your case...what are the values $\displaystyle a,b,$ and $\displaystyle c$?

8. a=100
b=64
c=16

9. Originally Posted by Annb
a=100
b=64
c=16
No. $\displaystyle a$ is always the number beside the squared variable. $\displaystyle b$ is always the number beside the first degree variable, and $\displaystyle c$ is always the constant term.

So

$\displaystyle a=-16$
$\displaystyle b=64$
$\displaystyle c=100$.

Do you understand?

Now, use the formula for finding the vertex. Do you know it?

10. is it -b/2a?

11. Originally Posted by Annb
is it -b/2a?
Very good. But, that's not the whole story. This will give you the time at which the object will reach its maximum height. So...what do you have to do once you have this time?

12. Ok, so I when I did the equation I got the answer -2. I just apply it to the equation and substitute t for -2 and i got 164!! The answer..

Thank you

13. Originally Posted by Annb
Ok, so I when I did the equation I got the answer -2. I just apply it to the equation and substitute t for -2 and i got 164!! The answer..

Thank you
Well... almost right. Let me ask you a question: Can time ever be negative? The answer is no (at least in this context).

$\displaystyle \frac{-b}{2a}=\frac{-(64)}{2(-16)}=\color{red}{+}2$.

Now, plugging back in we have

$\displaystyle s(2)=100+64(2)-16(2)^2$

$\displaystyle =100+128-64$

$\displaystyle =164$.

Sorry for being picky, but precision is key in mathematics.