Catching Coach:
OK, I have the definitive answer. It is always nice to have a rocket scientist handy. (My brother actually IS a rocket scientist.)
I posed the question to him, gave him my formula, and asked if calculus might give a better answer. Turns out is was about as I thought. His answer below:
Rob,
The answer is "yes, you can be more accurate, but not very much more..." Your linear approximation is a very good one in this example. A rigorous solution requires calculus.
We are given: V(x) = Vo - V'x
where, Vo = 75mph and V' = 0.1 mph/ft
Then the differential equation for the time of flight is
dt = dx/V(x)
which must be integrated between the limits of 0 to Xmax (Xmax = 130 ft)
Which gives
t = (-1/V') ln((Vo - V'Xmax)/Vo)
When you plug in all the numbers (including 1mph = 1.46666 ft/sec), you get
t = 1.297866...sec
Coach: The linear approximation both you and I worked out gave an answer of 130/100.466 = 1.294 seconds - a trivial difference from the answer using differential calculus.
Which is good news - it means you dont have to be a rocket scientist to get a close enough answer!