Angle and Range of Projectile Motion

[tharindu]

Using R=v^2sin2x/g how do you prove that the angle of 45 yields the maximum distance?

 

[thebigstar25]

for a given v (velocity) and since g(the gravity) is constant then the only variable that will affect the range (distance in the x-direction) is sin(2theta) , and the max. number can be obtained from sin(2theta) is 1 (since the range for the sin is between -1 and 1) ..

then you will have sin(2theta) = 1 >> 2theta = arcsin(1) >> 2theta= 90 >> theta = 45 ..

hopefully that was clear .. :)