Projectile Range Symmetry Proof

[peasant242]

Homework Statement

Prove that a projectile launched at angle @ has the same horizontal range as one launched with the same speed at angle (90 - @).

Homework Equations

Obviously kinematics will be used =/

The Attempt at a Solution

I've been messing around with kinematics but haven't gotten anywhere. I also know that sin(90-@) = cos(@) . Help appreciated :]

 

[Kurret]

let the initial speed be V, and decomposite into V_y=Vsin@ and V_x=Vcos@. Now use this to first calculate the time the projectile is in the air and then the range of the projectile.

 

[peasant242]

I appreciate the help but when you decomposite the V wouldn't it be:

V_y = sin(90-@)
V_x = cos(@)

 

[Kurret]

uhm no, you said yourself that sin(90-@)=cos@, so that would give V_y=V_x :)