# Collisions after effects!

4 identical spheres are seen above. Spheres C and D fall freely from a height $$h$$ before colliding with spheres A and B on the left and right sides as shown.If the acute angle between the line joining the centres of A and C and the vertical is $$\theta$$ and that for B and D with vertical is $$\alpha$$ .

If the time at which the velocity vectors of A and B are mutually perpendicular to each other is given by

$$\frac{\sqrt{2gh}( Pcosec2\alpha + \sqrt{Hcosec^{2}2\alpha-YsinS\theta sinI\alpha} )}{hsinC\theta sin S\alpha}$$

find $$P+H+Y+S+I+C+S$$

Details and Assumptions

• All collisions(including with vertical wall) are ELASTIC
• ALL spheres are identical
• path KL has a length $$h$$
• no rotation takes place
• entire motion is free of non conservative dissipative forces
• in case of finding two values of $$t$$, consider the larger value

this problem is part of the set "innovative problems in mechanics"

×