In the 1940s, the human cannonball stunt was preformed regularly by Emmanuel Zacchini for the Ringling Brothers and Barnum & Bailey Circus. The tip of the cannon rose 15 feet, and the total horizontal distance traveled was 175 feet. An equation of the parabolic flight has the for ax^2+x+c(b=1); use the given information to find an equation of the flight and the maximum height attained by the human cannonball

Answer: We're given that the parabolic flight follows theequation ax² + x + c, where 'a' and 'c' are constants we need to find. We know the parabola passes through two points: - (0, 15): The cannon's tip is 15 feet high (y-coordinate) at the starting point (x-coordinate 0). - (175, 0): The human cannonball lands 175 feet away (x-coordinate) at ground level (y-coordinate 0). Substitute the points into the equation ax² + x + c: - Point (0, 15): a(0)² + 0 + c = 15 This simplifies to c = 15 - Point (175, 0): a(175)² + 175 + c = 0 Substitute c = 15 into the second equation: a(175)² + 175 + 15 = 0 a(30625) = -190 a = -190/30625 = -38/6125 Now that we have 'a' and 'c', the equation of the parabolic flight is: y = (-38/6125)x² + x + 15 The maximum height occurs at the vertex of the parabola. The x-coordinate of the vertex of a parabola in the form ax² + bx + c is given by -b/2a. In our case, b = 1 and a = -38/6125: xvertex = -1 / (2 * (-38/6125)) = 6125/76 Now, substitute this x-coordinate back into the equation to find the y-coordinate (maximum height): yvertex = (-38/6125)(6125/76)² + (6125/76) + 15 yvertex ≈ 102.63 feet Therefore: - Equation of the flight: y = (-38/6125)x² + x + 15 - Maximum height attained: Approximately 102.63 feet

Answered by ethelgracecanicosa80 | 2025-03-24