When a projected object moves under the influence of a constant force (without air resistance), its path is parabolic. This occurs when a ball is thrown near the surface of a planet or other celestial body. Suppose two balls are simultaneously thrown upward at a 45° angle on two different planets. If their initial velocities are both 30 mph, then their paths can be modeled by the following equation.

Here g is the acceleration due to gravity, and x and y are the horizontal and vertical distances in feet, respectively. The value of g will vary depending on the mass and size of the planet.

(a) For Earth g = 32.2, while for Mars g = 12.6. Find the two equations, and graph on the same screen of a graphing calculator the paths of the two balls thrown on Earth and Mars. Use the window 30, 1804 by 30, 1004.

(b) Determine the difference in the horizontal distances traveled by the two balls to the nearest foot.

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