Math help needed

Question

Duffer McGee stood on a hill and used a nine iron to hit a golf ball that reached a maximum height of 149 feet and stayed in the air for 5.8 seconds before it touched the ground. 

Mercury has a gravity of approximately 12 feet per second squared compared to Earth's 32 feet per second squared. NASA did a simulation to try to determine how high the golf ball would fly and how long it would stay in the air on Mercury if it was hit at the same height, angle and velocity as Duffer's. The data below represent the results of that simulation: 

t	1	2	3	4	5
H(t)	112	181	238	283	316

Based on your model how high is the hill from which the golf ball was hit?

Answer 1

The quadratic regression for mercury

h(t) = -6t²+87t+31 = at²/2+v₀t+h₀

which would make the hill 31 feet high.

Also h_earth(t) = -16t²+87t+31

If you use the quadratic formula to solve for t for h(t)=0, t=5.7731 ≈ 5.8 seconds

----

If you don't want to do regression, you can use the first two data points to solve for v and h

-6+v+h = 112

-24+2v+h = 181

Subtracting the first equation from the second gives

-18+v=69 ==> v=87

-6+87+h=112 ==> h =31

Same answer

Answer 2

I used Desmos Graphing Calculator to do a quadratic regression (ax² + bx + c) and got a nice fit. Looks like maximum height on Mercury would be 346.38 feet after 7.25 seconds. In the regression a = -6, b = 87 and c = 31.

Can you duplicate with another method?