A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.8x^2+12x+25.8 where x is the horizontal distance in meters from the starting point on the roof and y is 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.

Question

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.8x^2+12x+25.8 where x is the horizontal distance in meters from the starting point on the roof and y is 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.

Answer 1

To find the horizontal distance the rocket will travel, we need to find the value of x when y=0 (the rocket hits the ground).

0=-0.8x^2+12x+25.8

We can simplify this equation by dividing by -0.8:

0.8x^2 - 15x - 32.25 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in a=0.8, b=-15, and c=-32.25:

x = (-(-15) ± √((-15)^2 - 4(0.8)(-32.25))) / 2(0.8)

x = 23.44 or x=2.06

Since the rocket is launched from a roof, we can disregard the negative value for x. Therefore, the rocket will land approximately 23.44 meters horizontally from its starting point. Rounded to the nearest hundredth, the answer is 23.44 meters.