SOLUTION: I have collected data has follows for a projectile we threw in class: Estimated launch height - 1.0m Estimated max height - 2.6m Estimated horizontal distance traveled

SOLUTION: I have collected data has follows for a projectile we threw in class: Estimated launch height - 1.0m Estimated max height - 2.6m Estimated horizontal distance traveled - 6.4m f

Question 1025681: I have collected data has follows for a projectile we threw in class:
Estimated launch height - 1.0m
Estimated max height - 2.6m
Estimated horizontal distance traveled - 6.4m
flight time - 1.33s
With this data, I want to make an equation in vertex form - y=a(x-h)2+k
Where y is the vertical distance traveled and x is the horizontal distance traveled. How would I complete the equation with that information?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since height as a function of time is given by:

where

is the initial VERTICAL velocity and

is the initial height, you can plug in your value for the total flight time,

and a

(since that was the height at the end of the 1.33 seconds), and then calculate

Once you have

, and recalling that the

-coordinate of the vertex of

is given by

, you can calculate the horizontal displacement of the highest point by:

Then, plugging values into your vertex form of a parabola, you get

The only thing left to do is find an appropriate value for a.

Since we know that when the horizontal displacement was zero, the vertical displacement was 1, so:

Solve for

I left all of the arithmetic for you to do yourself. Enjoy.

John

My calculator said it, I believe it, that settles it

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