In the illustration below, a rectangular coordinate system has been superimposed over a billiard table. Write a function that mathematically models the path of the ball that is shown banking off of the far cushion.
F(x)=
nice try.
To mathematically model the path of the ball banking off of the far cushion, we can use the concept of reflections. When the ball hits the far cushion, it reflects at an angle equal to the angle of incidence.
Let's assume the ball starts at point A(x1, y1) and it is traveling towards the far cushion. The equation for the line representing the far cushion is y = const, where const is the y-coordinate of the cushion.
First, we need to determine the slope of the line representing the ball's path before it hits the far cushion. This can be done by calculating the slope between points A(x1, y1) and B(x2, y2), where x2 is some point on the far cushion.
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1)
Now that we have the slope, we can calculate the y-intercept (b) of the line representing the ball's path before hitting the cushion using the formula: b = y1 - m * x1
With the slope and y-intercept, we can define the equation for the line representing the ball's path before hitting the cushion:
f(x) = mx + b
This equation gives you the mathematical model for the path of the ball before it hits the far cushion.