- #1
stoffer
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Here is my problem, can anyone help me out?
Prove the maximum range of a skier going down a ski jump is given by
(theta) = 45degrees - phi/2 , where theta = optimal launch angle , phi = slope angle of take off with respect to the incline of the hill.
I have the following equations to use
Xf = Vi*cos(theta)*t = d*cos(phi)
Yf = Vi*sin(theta)*t - (1/2)g*t^2 = -d*sin(phi)
Where, Xf= final x component, Yf= final y component, Vi = velocity at launch, t= time jumper is in air, g= grav. constant, d = distance traveled along the inlcine of the hill
I am trying to eliminate t in the above equations and then differentiate to maximize d in terms of theta.
Any ideas how to do this? What is a good first step? Any help you can give will be greatly appreciated.
Thanx
Prove the maximum range of a skier going down a ski jump is given by
(theta) = 45degrees - phi/2 , where theta = optimal launch angle , phi = slope angle of take off with respect to the incline of the hill.
I have the following equations to use
Xf = Vi*cos(theta)*t = d*cos(phi)
Yf = Vi*sin(theta)*t - (1/2)g*t^2 = -d*sin(phi)
Where, Xf= final x component, Yf= final y component, Vi = velocity at launch, t= time jumper is in air, g= grav. constant, d = distance traveled along the inlcine of the hill
I am trying to eliminate t in the above equations and then differentiate to maximize d in terms of theta.
Any ideas how to do this? What is a good first step? Any help you can give will be greatly appreciated.
Thanx