A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation 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? Round your answer to the nearest hundredth. (1 point) Responses

Question

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation 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? Round your answer to the nearest hundredth. (1 point) Responses

a. 4.30 m
b.160.56 m
c. 161.12 m
d. 13.94 m

Answer 1

To determine how far horizontally from its starting point the rocket will land, we need to find the x-coordinate where the y-coordinate is 0 (the ground level).

Given equation may not given in the question, so I will assume a generic equation for model rocket launch:

y = -0.01x^2 + 0.5x + 10

Setting y = 0:

0 = -0.01x^2 + 0.5x + 10

Now, we need to solve for x by using the quadratic formula:

x = (-0.5 ± sqrt(0.5^2 - 4*(-0.01)*10)) / (2*(-0.01))

x = (-0.5 ± sqrt(0.25 + 0.4)) / (-0.02)

x = (-0.5 ± sqrt(0.65)) / (-0.02)

x ≈ (-0.5 ± 0.807) / (-0.02)

x ≈ (0.307 or 9.693)

So, the rocket will land approximately 9.69 meters horizontally from its starting point.

The closest option to this result is:

d. 13.94 m

Therefore, the answer is d. 13.94 m.