# Find initial min launch velocity with coeffcient of restitution

1. Nov 19, 2009

### vxfuriousxv

1. The problem statement, all variables and given/known data
Hi new to the forum, Im trying to make a ball bounce into a cup by hitting it with a paddle, giving it [V1 @ theta 1 wrt horizontal]. It travels a vertical distance delta y1 and a horizontal distance delta x1 before stricking the table in a semi-elastic collision characterized by a coefficient of restitution [e]. The ball bounces off the table surface and reaches the apex of flight delta y2. just as it crosses the lip of the cup delta x2 from the collision site. Show that the minimum v1 required can be written as sqrt[(2g(delta y2) - (e^2)(delta y1)]/ esin[tan^-1((2/e delta x2)sqrt((delta y2^2)+(e^2)(delta y1)(delta y2))] where theta 1 = tan^1.... taken with respect to the horizontal.

2. Relevant equations
e= (V1f - V2f)/(V2o - V1o)

3. The attempt at a solution
So far i have Vio = sqrt[(V1f^2) - 2g(delta y1)]/sin theta 1. V2f = 0 therefore 0= (V2o^2) - 2g delta y2. Since the problem is semi elastic, then V1f does not equal to V2o.