A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the
equation y = 0.04x + 7.1x + 7.2, 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?
the rocket is on the ground when y = 0
it seems like one of the x terms should be an x^2 term...
Fix your equation, and then solve for x when y=0
That is when it hits the ground, right?
To find the horizontal distance at which the rocket will land, we need to determine the value of x when y equals zero. This means we need to solve the equation:
0.04x + 7.1x + 7.2 = 0
To solve this equation, we can combine like terms:
7.14x + 7.2 = 0
Next, we isolate the variable x by subtracting 7.2 from both sides of the equation:
7.14x = -7.2
Now we can solve for x by dividing both sides of the equation by 7.14:
x = -7.2 / 7.14
Using a calculator, we find that x is approximately -1.007 meters.
In this context, negative values for x do not make sense, as it represents a distance in meters from the starting point on the roof. Therefore, we disregard the negative value of x.
Hence, the rocket will land approximately 1.007 meters horizontally from its starting point.