I would like to calculate the bounce of an object given three components: Force on impact, Mass and Velocity. What I mean is the following: When an object falls from a height, $\ V_0 = 0$, and $\ g=9.8$, in time 2 seconds with a mass of 50g, how would I work out the bounce when it hits a perfectly flat, friction less surface? And furthermore, a function would be even better like: $\ b(x) = something$ where $\ x$ is a point on that bounce.
Any answers would be very helpful.
Before the collision with the surface, the vertical velocity is given by $$v_1=V_0-gt_i=-gt_1$$ pointing downward. Immediately after the collision, the velocity will be pointing upwards, with $$v_2=-ev_1=egt_1$$ I've used positive direction upwards and $t_1=2s$. From here you can calculate the trajectory after the bounce.