SOLUTION: challenge: Challenging problems : please help Major League Baseball is putting an expansion team on Mars. Because of Mars� Lower gravity, baseballs travel farther and higher

Question 935431: challenge:
Challenging problems : please help
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.

Answer by brysca(112) (Show Source): You can put this solution on YOUR website!
Yes, I understand this is a late response, but I could not bare to see someone go through all that trouble of typing the question without an answer lol. So here you go, if you have any questions don't be afraid to ask.

.
hope this helps!
Response to second student comment: The short answer is that the 45 degree angle is actually just extra information put into the problem. The problem can actually be solved without even knowing the angle of launch.
The long answer:

.
Also, in the equation I mentioned, Yo stands for the initial vertical position of the ball, which would be 3 feet from the ground in this case.
I hope this clarified at least some of the confusion you may have had. This subject matter is usually covered in Physics classes over the course of a week, so I really gave a crash course on it.
Extra information on what I was talking about here: http://www.ux1.eiu.edu/~cfadd/1150/03Vct2D/proj.html
A LOT more information
http://content.njctl.org/courses/science/ap-physics-b/kinematics-2/kinematics-presentation-2/kinematics-presentation-2014-09-22-1-slide-per-page.pdf
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