Major League Baseball is putting an expansion team on Mars. Because of Mars’ lower gravity, baseballs travel farther and higher than they do on Earth, and the domed stadium that will house the new Mars Dusties franchise must reflect this.
On Earth, the distance from home plate to center field wall is 400 feet, and a baseball hit at a 45 degrees angle with a velocity of 112.72 ft/sec will hit the base of the center field wall. The path of this baseball can be modeled by two quadratic equations:
Y= -g(t^2)/2 + 79.705t +3 and y = – g (x^2)/12705.8 + x +3
The first equation gives the height of the ball ,y, in feet with respect to time ,t, in seconds, while the second gives the height with respect to horizontal position,x, in feet. On Earth, g=32, but on Mars, g = 12.17.
1-If the baseball is hit with the same angle and velocity on Mars as on Earth, how far from home plate should the center field wall will be for the ball to hit its base (to the nearest foot)? Hint :use the Quadratic Formula.
2- The stadium designers want the dome to have 50 feet of additional clearance. Above the maximum height of the baseball. What is the height of the dome?
3-Is the increased distance to be covered in the outfield approximately proportional to the increased hang time of the ball? For example, does doubling the distance traveled by the ball also doubled the hang time of the ball? Justify your answer.