Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Isaiah decides to launch a model rocket to demonstrate parabolic motion. Given x stands for time and y stands for height in feet, find the equation for his rocket if it launches at 5 seconds, lands at 11 seconds, and is at 80 feet after 10 seconds. Explain in one sentence how you created your equation.

Sagot :

MrRoyal

The parabolic motion is an illustration of a quadratic function

The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31

How to model the function?

Given that:

x stands for time and y stands for height in feet

So, we have the following coordinate points

(x,y) = (5,0), (11,0) and (10,80)

A parabolic motion is represented as:

y =ax^2 + bx + c

At (5,0), we have:

25a + 5b + c = 0

c= -25a - 5b

At (11,0), we have:

121a + 11b + c = 0

Substitute c= -25a - 5b

121a + 11b -25a - 5b = 0

Simpify

96a + 6b = 0

At (10,80), we have:

100a + 10b + c = 80

Substitute c= -25a - 5b

100a + 10b - 25a -5b = 80

75a -5b = 80

Divide through by 5

15a -b = 16

Make b the subject

b = 15a + 16

Substitute b = 15a + 16 in 96a + 6b = 0

96a + 6(15a + 16) = 0

Expand

96a + 90a + 96 = 0

This gives

186a = -96

Solve for a

a = -16/31

Recall that:

b = 15a + 16

So, we have:

b = -15 * 16/31 + 16

b =-240/31 + 16

Take LCM

b =(-240 + 31 * 16)/31

[tex]b =256/31

Also, we have:

c= -25a - 5b

This gives

c= 25*16/31 - 5 * 256/31

Take LCM

c= -880/31

Recall that:

y =ax^2 + bx + c

This gives

y = -16/31x^2 + 256/31x - 880/31

Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31

Read more about parabolic motion at:

https://brainly.com/question/1130127

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.