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.
((x) = -0.05(x° - 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

The given polynomial that describes the path of the cannonball is:

h(x) = -0.05(x^2 - 26x - 120)

where h(x) represents the height of the cannonball at a horizontal distance of x feet from the cannon.

To find where Nik will land, we need to find the value of x when h(x) = 0, since this indicates that the cannonball has landed on the safety net.

So we need to solve the equation:

-0.05(x^2 - 26x - 120) = 0

Simplifying this equation, we get:

x^2 - 26x - 120 = 0

We can use the quadratic formula to solve for x:

x = (-(-26) ± sqrt((-26)^2 - 4(1)(-120))) / 2(1)

x = (26 ± sqrt(976)) / 2

x = 13 ± 2sqrt(61)

So the cannonball will land either 13 + 2 sqrt (61) feet from the cannon or 13 - 2 sqrt (61) feet from the cannon.

Since 30 feet is the only distance given in the problem, we can't determine which solution is correct. Therefore, we can conclude that the function does not give us enough information to tell us where Nik will land.

Explanation: