Question

A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t)= -16t2 + 40ft + 1.5. Find the maximum height attained by the ball.

Answer 1

\(\tt{x=\dfrac{-b}{2a}}\)

Answer 2

\[\frac{ -b }{ 2a}\] \[\frac{ -40 }{ -32 }\]
Time = 8

Answer 3

What is your equation exactly?

Answer 4

\(h(t)= -16t^2 + 40t + 1.5\) ?

Answer 5

the max height will be the vertex (because the parabola opens down, and that is because the leading coefficient is negative)

Answer 6

I need to find the maximum height. Yes, that's the equation. So my time is 8, right? To find my height, plug 8 in.

Answer 7

You don't need the height, if you are given that function you can find the vertex and that will be your maximum height.

Answer 8

To find max height, I need to first obtain the time it takes the ball to reach it, then plug in t.

Answer 9

how did you get time = 8?
\(\tt{\dfrac{-40}{-32}=1.25}\) not 8

Answer 10

I got 8 because my calculator is autistic and I am jut realizing this.

-16(1.25)^2 + 40(1.25) + 1.5
-25 + 50 + 1.5
25 + 1.5

Height = 26.5

Answer 11

maximum height is 26.5
you get the time 1.25 and plug it in for t

Answer 12

Thanks! I got it :) `

Answer 13

when you use \(\tt{x=\dfrac{-b}{2a}}\), you find the time
then you plug the time in for the variable
and yw :]

Answer 14

\(\large\color{black}{ \displaystyle h(t)=-16t^2-40t+1.5 }\)
\(\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t)+1.5 }\)

side caclulation:
\(\large\color{black}{ \displaystyle 2.5\div2=1.25 }\)
\(\large\color{black}{ \displaystyle 1.25^2=1.5625 }\)

\(\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t+1.5625-1.5625)+1.5 }\)
\(\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t+1.5625)+(-16)(-1.5625)+1.5 }\)
\(\large\color{black}{ \displaystyle h(t)=-16(t+1.25)^2+25+1.5 }\)
\(\large\color{black}{ \displaystyle h(t)=-16(t+1.25)^2+26.5 }\)

So the height is 26.5 and it occurs at t=1.25.

Answer 15

(via completing the square)

Answer 16

I never learned how to complete squares :(

Answer 17

Okay, so can I shoot one more at you guys?

Answer 18

don't you learn completing the square in Alg 1?

Answer 19

I don't think there is a single particular order for learning different concepts in math.... I have seen people who asked how to find a slope in DE section.

Answer 20

Well, completing the square is something that you can probably browse and find a good resource quite fast:)