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 μ\mu and released his body from rest, so that it leaves the Parabolic(y=x2y=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 RR is such that , boy will Just fall in the swimming pool. If it is expressed as :

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

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

Find m+n+p+qm+n+p+q

Details and assumptions

  • μ=0.5g=10m/s2H=0.75mh=0.5m\displaystyle{{ \mu =0.5\\ g=10m/{ s }^{ 2 }\\ H=0.75m\quad \\ h=0.5m }}

  • e is Euler's constant.

Try more Deepanshu's Mixing of concept.
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