An artillery gun on a battle ship is capable of launching a shell at a vertical velocity of 400 m/s. A target is 40 Km away and 500 m above the ground.

Question

what is the maximum range the target can be away from the gun if the target is 500 m above the ground?

Answer 1

Max range is usually at a 45 degree angle but in this case I'm not sure because of the elevation. Well it can't be solved otherwise so
500 = 400sin45t - 4.9t^2
Solve the quadratic for t
x = 400cos45t