Stuck on this test question

[michaelscarnnn]

At the national spitting competition contestants were lined up on top of a tall building.
The winning projectile was projected off the top of the building in a trajectory defined by the
equation:

h=-4.9(x-3)^2 + 82 ............................................................................. (edited)​

where height(h) in metres and time (x) in seconds. ​

a) What is the maximum height above the ground that the projectile reached? ​

b) How long did it take to reach the maximum height?

c) Find the height of the building. Show your work! ​

d) How long was the projectile in the air before it hit the ground? (5 marks)

(Nearest 10th of a second)(Hint: substitute h=0)​

 

[yoscar04]

You should show what you have tried so far.

 

[Steven G]

You should give us h(t)!

 

[michaelscarnnn]

You should give us h(t)!

Sorry I completely forgot to add this part given with the question!
h=-4.9(x-3)^2 + 82

 

[yoscar04]

Sorry I completely forgot to add this part given with the question!
h=-4.9(x-3)^2 + 82

Did you mean h=-4.9(t-3)²+82? Do you know what is special about being at the maximum height?

 

[michaelscarnnn]

Did you mean h=-4.9(t-3)²+82? Do you know what is special about being at the maximum height?

No, that is how it was given since in the question time is represented by x. The maximum height would be the vertex of the parabola that this situation represents I think. I'm quite confused.

 

[Otis]

Sorry I completely forgot to add this part given with the question!
h=-4.9(x-3)^2 + 82

Hi michael. I was just about to ask, heh. Let's start with part (a), which asks about the vertex point.

For part (a), do you recognize that they've written the quadratic equation in vertex form? (Your class may use a name different than 'vertex form', but I'm talking about the form where we can see the vertex coordinates displayed in the equation itself.)

If you're not sure what I'm talking about, then let us know.

?

 

[Otis]

Did you mean h=-4.9(t-3)²+82? …

Hi yoscar. The symbol x is given, as the independent variable.

?

 

[yoscar04]

Hi yoscar. The symbol x is given, as the independent variable.

?

Yes, I missed the text where it says x is the time. In any event it is really confusing to call h(t), I mean their h(x), the equation of the trajectory. I teach physics and I can't recall writing such a thing h(x) instead of h(t).

 

[Otis]

Yes, I missed the text where it says x is the time … I can't recall writing such a thing h(x) …

Ah -- I'd thought that maybe it was Jomo's reply that had thrown you off.

This type of exercise is often assigned in algebra courses where neither function notation nor the concept of 'function' has yet been introduced. I've seen similar exercises where they use y instead of h, to represent the dependent variable. It wouldn't confuse me to see additional symbols used for height and time, either.

?

 

[yoscar04]

Ah -- I'd thought that maybe it was Jomo's reply that had thrown you off.

This type of exercise is often assigned in algebra courses where neither function notation nor the concept of 'function' has yet been introduced. I've seen similar exercises where they use y instead of h, to represent the dependent variable. It wouldn't confuse me to see additional symbols used for height and time, either.

?

Actually I was happy with Jomo's h(t) and asked to consider h(t) and not h(x). I should get used to the fact that it is a problem from a math class.

 

[Steven G]

Did you mean h=-4.9(t-3)²+82? Do you know what is special about being at the maximum height?

I messed up by saying h(t) instead of h(x).

 

[HallsofIvy]

The height is given by \(\displaystyle h= -4.9(x- 3)^2+82\). Do you understand that a square is never negative? So h is 82 minus some number. That should tell you immediately what is the largest possible value of h!