- #1
throneoo
- 126
- 2
Hi guys,
I was working on a formula for the optimal angle for simple point-like projectiles free-falling under a uniform g-field but I got stuck.
after a simple derivation , I obtained the following equation:
R=(vcos(@)/g)(vsin(@)+((vsin(@))^2+2gh)^0.5)
where R , @ , h are respectively the range as it reaches the ground , launch angle and initial height
I then took a derivative w.r.t. @ and set dR/d@ =0 , and obtained the following equation:
vsin^2(@)+ksin(@)=vcos^2(@)+(v^2sin(@)cos^2(@))/k
where k=((vsin(@))^2+2gh)^0.5
I'm quite certain that I got everything right as when h=0 , the equation reduces to tan(@)^2=1 and immediately yields @=pi/4
but with a non-zero 'h' I fail to see how I can solve for @ in terms of the parameters via normal algebraic methods..
How else can I work on it ?
I was working on a formula for the optimal angle for simple point-like projectiles free-falling under a uniform g-field but I got stuck.
after a simple derivation , I obtained the following equation:
R=(vcos(@)/g)(vsin(@)+((vsin(@))^2+2gh)^0.5)
where R , @ , h are respectively the range as it reaches the ground , launch angle and initial height
I then took a derivative w.r.t. @ and set dR/d@ =0 , and obtained the following equation:
vsin^2(@)+ksin(@)=vcos^2(@)+(v^2sin(@)cos^2(@))/k
where k=((vsin(@))^2+2gh)^0.5
I'm quite certain that I got everything right as when h=0 , the equation reduces to tan(@)^2=1 and immediately yields @=pi/4
but with a non-zero 'h' I fail to see how I can solve for @ in terms of the parameters via normal algebraic methods..
How else can I work on it ?