A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2+ 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
A. 208.02 m
B. 416.03 m
C. 0.52 m
D. 208.19 m
I keep coming up with 208.17....So that means the answer is A correct?
yes ... A is the correct answer ... even though your solution is closer to D
Thank you!
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
lol
Well, it seems like you're really close to the answer! But let me ask you this - have you considered the gravitational forces acting on the rocket as it descends? Remember, when the rocket hits the ground, its height will be zero. So, to find the horizontal distance it will land, you can set the equation equal to zero and solve for x. Give it another shot, and remember, "rocket" science can be a blast!
To find the horizontal distance at which the rocket will land, we need to find the x-coordinate when the rocket hits the ground. In other words, we need to find the value of x when y equals 0.
Given the equation: y = -0.04x^2 + 8.3x + 4.3
Setting y equal to zero: 0 = -0.04x^2 + 8.3x + 4.3
To solve this quadratic equation, we can factor it or use the quadratic formula. However, the equation doesn't factor easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -0.04, b = 8.3, and c = 4.3.
Substituting these values into the quadratic formula:
x = ( -8.3 ± √(8.3^2 - 4(-0.04)(4.3)) ) / (2(-0.04))
Simplifying further:
x = ( -8.3 ± √(68.89 + 0.688) ) / (-0.08)
x = ( -8.3 ± √69.578) / (-0.08)
Now, let's calculate the two possible solutions:
x₁ = ( -8.3 + √69.578) / (-0.08)
x₂ = ( -8.3 - √69.578) / (-0.08)
Using a calculator, we find:
x₁ ≈ 0.52
x₂ ≈ 208.02
Therefore, the rocket will land approximately 208.02 meters horizontally from its starting point.
So, the correct answer is A. 208.02 m