**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.