is it possible to calculate the maximum altitude of a projectile when you are given only the range?

Answer 1

Not positive, but you could try doing this (I'm sure there's a simpler way, but I just go with whatever equation first pops in my mind).

v^2=v(intial)^2 + 2a * (range)

The v would be 0 since it would have landed, a is 9.8 (positive or negative according to you, I always use negative because it's gravity and gravity pulls down, but you can make it positive by relativity), and then use the range.

Then plug that into the formula v= v(intial) + at

Then take half the time and use this formula:

x= x (intial) + v(intial) * t + .5a * t^2

I think that would work, but I'm sure there's a simpler way.

Answer 2

It's not possible to find the maximum height with only the range. In fact the modern self-propelled howitzer can fire off six rounds which will hit the same target simultaneously.

One example of the increased firepower provided by modern mobile howitzers is the latest version, the G6-52, of the 155 mm G6 howitzer. It can fire up to 6 rounds in quick succession which will land near simultaneously. This is achieved by firing the shells at different trajectories so that the first round has the longest flight time and the last round the shortest; made possible by an automated ammunition feed system.

Answer 3

One cannot find H if R alone is given. One more quantity is needed.
If at least θ is given one can find H from
H = 4R / tan θ