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 = -0.048x + 4.1x + 7.6, 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. 1.82 m
b. 208.64 m
c. 10432 m
d. 104.93 m

Answer 1

To find the horizontal distance from the starting point where the model rocket will land, we must set the equation y = -0.048x2 + 4.1x + 7.6 to zero and solve for x using the quadratic formula. This will give us two possible values for x, of which the positive one is the correct answer, since the rocket cannot land a negative distance away.

Step-by-step explanation:

The question asks us to find how far horizontally a model rocket will land from its starting point, given the quadratic equation that models its path, y = -0.048x2 + 4.1x + 7.6. To find the horizontal distance (x) where the rocket will land, we must set y to zero and solve for the positive value of x, as this will indicate the point where the rocket hits the ground.

First, we set up the equation with y equal to zero: 0 = -0.048x2 + 4.1x + 7.6. This is a quadratic equation that we can solve by using the quadratic formula, or by factoring if it is factorable. In this case, the easiest method is using the quadratic formula:

x = −(b / 2a) ± √(b2 − 4ac) / 2a,

where a = -0.048, b = 4.1, and c = 7.6. Substituting these values in, we calculate the possible values of x.

After calculating, we find that one of the x values is negative, which isn't realistic for our scenario since the rocket can't land a negative distance away, and the other x value is positive. The positive value gives us the answer for where the rocket lands horizontally from the starting point.