Projec-ception

A point mass is projected at an angle \(\frac{\pi}{3}\) radians from the horizontal. It collides at its maximum height, with a sphere of diameter 72.5 cm. such that it is projected off the sphere, again at an angle \(\frac{\pi}{3}\) radians from the horizontal. The sphere, due to the collision, is bounced off the floor. The point mass, in its descent, collides with the sphere again, through the same horizontal of the previous point-mass-sphere collision, and is projected at an angle \(\frac{\pi}{6}\) radians below the horizontal. If the density of the sphere is \(50\) kg m\(^{-3}\) and uniform mass distribution, then the mass of the point-mass is \(m\), and its initial velocity is \(u\). Find \(\lfloor m+u \rfloor\). Assume all the collisions are elastic, and the sphere is rigid.

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