Final answer:
The maximum height that the ball reaches on this bounce is 6.45 meters.
Step-by-step explanation:
The maximum height that the ball reaches on this bounce can be determined by finding the y-coordinate of the vertex of the parabolic path. The equation for the parabolic path is y = -0.2x^2 + 5.8x - 35.6. To find the x-coordinate of the vertex, we can use the formula x = -b/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = -0.2 and b = 5.8. Plugging these values into the formula, we get x = -5.8/(2*(-0.2)) = 14.5.
Now, to find the maximum height, we substitute the x-coordinate of the vertex (14.5) back into the equation. y = -0.2*(14.5)^2 + 5.8*(14.5) - 35.6 = -0.2*210.25 + 84.1 - 35.6 = -42.05 + 84.1 - 35.6 = 6.45.
Therefore, the maximum height that the ball reaches on this bounce is 6.45 meters.