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Question: find out the optimal angle regarding the best ski jump

Question:find out the optimal angle regarding the best ski jump

laporte bernard 45 Maple 12
diff max
December 06 2012
2

assuming the skier is projected at an angle theta with respect to the horizontal over a landing incline sloped with an arbitrary angle phi :

xf = (vi*cos(theta)*t=d*cos(phi)

yf=(vi*sin(theta)*t-1/2*g*t^2=-d*sin(phi)

 

By eliminating the time t between these two equations and using differentiation to maximize d in terms of theta,

we should arrive at the following equation for the angle theta that gives the maximum value of d :

 

theta = 45° -phi/2  (Answer from a text book)

 

How can I handle that problem about ski jump with MAPLE  ?
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