Undergrad Angle of projection for maximum range

[Abhishek332211]

Hi,
I can't seem to work out how angle of projection for maximum range comes out to be (pi/4 - Beta/2)

This happens when the projectile is protected up the inclined plane.

Similarly, I couldn't understand how the angle comes out to be (pi/4 + Beta/2) when the projectile is protected down the inclined plane.

And the other two formulas that have been marked off.

Thanks in advance

 

[ZapperZ]

When the projectile is shot onto a flat ground, do you know how to find the angle for maximum range?

The method is identical here. You are given "R", the range of the projectile. Only this time, you are dealing with two angles, the angle for the initial velocity, and the angle of the inclined plane. For a fix angle of the inclined plane, how would you use "R" to find maximum "R" with respect to the projectile initial angle?

Zz.

 

[cnh1995]

Have you studied differentiation yet?