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I am trying to implement a Physics computer simulation (only basic) designed for children learning about forces. One of the sub games that i have created is to fire a character from a cannon and find the optimum angle, which ends up at 45 degrees.

However, the second sub game models drag force on the projectile, taking into account its mass, area, drag coefficient, and the air density. The equations are solved using an RK4 method. Excuse my lack of knowledge on this subject, but I am not that hot on physics, i just have an interest which is why i decided to model this simulation as my final university project as a computing student. Now, the question i have is that ive always understood that 45 degrees is the optimum angle to travel the farthest, but when simulating the drag projectile, the optimum angle is now 35. Is this correct, in that 45 degrees would no longer be optimum, or am i going wrong somewhere?

Many thanks