Projectile Motion and the Range Formula

[tharindu]

Hey Guys

Im wondering if anyone could help me simplify the range formula for projectile motion. So far I've got R=2v^2 sin(theta) cos(theta)/g.

Help will be appreciated. Thanks

 

[ideasrule]

Have you seen the identity sin(2x)=2sinxcosx?

 

[tharindu]

No i havent

 

[ideasrule]

Using that identity, you can simplify the range formula easily.

Note that the identity can be derived from sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Set a=b and you get sin(2a)=sin(a)cos(a)+sin(a)cos(a)=2sin(a)cos(a)

 

[tharindu]

so then the formula simplifies down to
R= v^2 sin(2x)/g ?