Question

Scenario: The Cannon Instructions: View the video found on page 1 of this Journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations. The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will travel follows a parabolic arch that can be described by this polynomial. f(x) = –0.05(x2 – 26x – 120) He is supposed to land on a safety net 30 feet away. Does the function give you enough information to tell you where he will land? If so, how far from the cannon will he land?

Answer 1

Answer:

Part A

Yes

Part B

He will land at a point 30 meters from Cannon

Step-by-step explanation:

Part A

The given function that represent the path of the Cannon, which is the path of a parabolic arc, is presented as follows;

f(x) = -0.05·(x² - 26·x - 120)

We note that the height, 'h', of the path of a parabola at a horizontal distance, 'x' from the origin is equal to f(x)

Therefore, given that at the ground level, at the start and end of the flight, the f(x) = 0, we can write;

-0.05·(x² - 26·x - 120) = 0

∴ x² - 26·x - 120 = 0

x = (26 ± √((-26)² - 4 × 1 × (-120)))/(2 × 1)

Which gives;

x = 30 or x = -4

Therefore, he lands at a point 30 meters from the starting point

Therefore, the function gives enough information to tell where he will land

Part B

He lands at the point, x = 30 from the point the cannon was fired.