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.

Try more Deepanshu's Mixing of concept.

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