# Fearless Boy says ''Let's do some different"

An fearless boy , want to do stunt . He reach on the top of rough fixed riding track which has coefficient of friction $$\mu$$ and released his body from rest, so that it leaves the Parabolic($$y=x^2$$) riding track at the origin, and then finally wish to fall in swimming pool, so that he doesn't hurt.

If value of $$R$$ is such that , boy will Just fall in the swimming pool. If it is expressed as :

$${ R=\sqrt { { me }^{ -\cfrac { \pi }{ n } }-\cfrac { p }{ q } } \\ }$$

here $$m,n,p,q$$ are positive integers and with $$p,q$$ coprime.

Find $$m+n+p+q$$

Details and assumptions

• $$\displaystyle{{ \mu =0.5\\ g=10m/{ s }^{ 2 }\\ H=0.75m\quad \\ h=0.5m }}$$

• e is Euler's constant.

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