Simple question about projectile motion

[Saladsamurai]

I recently helped someone in the homework forum with a problem that asked him to hit a target 8 miles away using a cannon or some other device involving projectile motion. Essentially, all we had to do was choose an initial angle and an initial velocity that would correspond to said angle that would reach a certain range R=8miles. Now my question is: we choose pi/4 as the initial angle because it is the most efficient; are there an infinite amount of combinations of initial velocities and angles that will reach a given range R ?

 

[trajan22]

I guess you could say that but the path and final velocity would be different for each angle. The problems I have always dealt with specify how to pick the angle, but if we are neglecting air drag and the curvature of the Earth then 45 degrees would be probably be the best angle to chose.

 

[Saladsamurai]

In this specific example we were neglecting air resistance and curvature.

 

[trajan22]

You are right though that any angle is valid. Though pi/4 is the most efficient choice.