Speedy, the human fly, is shot from a cannon whose opening is 12 feet high. After 2 elapsed seconds, Speedy is 108 feet in the a

Question

2 years ago

8

Speedy, the human fly, is shot from a cannon whose opening is 12 feet high. After 2 elapsed seconds, Speedy is 108 feet in the a

ir. After 3 elapsed seconds, Speedy is again 108 feet in the air. Which of the following is the best representation of the quadratic function modeling Speedy’s height, h(t), as a function of elapsed time, t?

Mathematics

1 answer:

wariber [46] · Answer 1 · 2022-12-27T21:55:47+03:00

The graph of Speedy's height in the air with time, which is based on a

quadratic function is a parabola.

The quadratic function modelling Speedy's height is given by the option; h(t) = -16·t² + 80·t + 12

Reasons:

The given parameters are;

The height of the cannon = 12 feet

Speedy's height after 2 seconds = 108 feet

Speedy's height after 3 seconds = 108 feet

Required: To select the best representation of the quadratic modelling Speedy's height, h(t), as a function of elapsed time, t?

Solution:

The path of Speedy's motion is a parabola

From the question, we have, that the initial height, at t = 0 is the height of the cannon = 12 feet

Therefore;

The equation has a constant term of 12

Given that the time it takes Speedy to rise above 108 feet and return to 108 feet = 3 - 2 = 1 second, we have;

The maximum height occurs between the 2nd and the 3rd second.

The path of a parabola is symmetric about the maximum point, therefore;

The maximum point occur at time $\displaystyle 2 \, s + \frac{3 - 2}{2} \, s = 2.5 \, s$

Therefore, the x-coordinate of the vertex is t = 2.5 s

From the general equation of a parabola, a·x² + b·x + c, the x-coordinate of the vertex is; $\displaystyle \mathbf{ -\frac{b}{2 \cdot a}}$