The town of gettysburg, PA, plans to shoot a live cannon as part of their annual Gettysburg Civil War Battle Reenactment. The organizers want to make sure that when they fire the cannon, it lands in a location that does not injure any participants or spectators. The slope of the field they are firing into can be represented by the equation y=0.15x. Let x represent horizontal distance, and y represents vertical distance.. if the cannon fires the cannon ball at an arc denoted by the equation y=-0.5x^2+2.5x+1, at what distance will the cannonball land. -I know i'm supposed to set -0.5x^2+2.5x+1=.15x and use distance formula BUT I KEEP GETTING DIFFERENT ANSWERS.

The cannonball lands at approximately 5.093 unit distance from the point of fire

Step-by-step explanation:

The given parameters are;

The arc denoting the equation of motion of the cannon is y₁ = -0.5·x² + 2.5·x + 1

The slope of the field where in the direction the cannon is fired is y₂ = 1.5·x

The points where the cannonball land on the slopping field is given as rightly pointed by equating the two equations, the cannonball path path and the field path as follows;

At the point of contact of the cannonball and the field, the y-values of both equation will be equal

y₁ = y₂

∴ -0.5·x² + 2.5·x + 1 = 0.15·x

Which gives;

-0.5·x² + 2.5·x - 0.15·x + 1 = 0

-0.5·x² + 2.35·x + 1 = 0

-(-0.5·x² + 2.35·x + 1) = 0.5·x² - 2.35·x - 1 = 0

0.5·x² - 2.35·x - 1 = 0

The above equation is in the general form of a quadratic equation, which is given as follows;

a·x² + b·x + c = 0

By the quadratic equation, we have;

Plugging in the values, gives;

∴ x ≈ 5.093 or x ≈ -0.393

Therefore, the cannonball will takeoff at x ≈ -0.393 and land at x ≈ 5.093

The height from which they fire the cannon is given by the substituting the value of x ≈ -0.393 into the equation for the path of the cannonball, to give;

= -0.5·(-0.393)² + 2.5·(-0.393) + 1 = -0.0597

≈ -0.0597.

However, the actual initial height from which the cannonball is fired given by placing x = 0, which gives y = 1, which is the reason for the other (negative) value for x. Please see the attached graph created with Microsoft Excel.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

c

step-by-step explanation: