whats the bounce height of a ping pong ball falling from a height of 20cm -270cm?

Question

try to include all the input variables and out put variables and terminal velocity

Answer 1

You don't include enough information to answer this really definitively... bouncing a ping pong ball on concrete will be different from a linoleum tile floor or a rubber mat (and probably won't bounce at all on a carpet, even if the pile is pretty short). Altitude or barometric pressure might also influence it slightly due to differences in air resistance with changes in air density.

Therefore, the only thing you could say is that if it fell in a vacuum against a hard, frictionless surface such that there was a 100% elastic collision (momentum conserved), it would bounce back up to its starting height before gravity slowed it back down and it would fall back down again, forever. Of course, in real life, there is no frictionless surface, so it would be slightly inelastic... I'm afraid I can't calculate it without a LOT more research into the coefficient of friction of various surfaces, the air resistance against a standard 4 cm diameter ping-pong ball, etc...

Answer 2

Assuming a perfectly eleastic collision then all momentum is conserved. Thus the ping pong ball will bounce back to the height from which it was dropped.
Of course no real collision is perfectly elastic so some energy will be lost. However there is no practical way to calculate how much. You could perhaps make a stab at it by assesing all the input variables as you say.
Input variables would include the surface roughness of the ping pong ball, air density, proximity to the equator, elasticity and bulk modulus of the ping pong ball. I highly doubt that terminal velocity would be any factor worth considering since not enoug drag force could be achieved over a drop of 270 cm
Of course it would take you weeks to work out all the calculations, or you could just drop the ping pong ball a few times and measure how high up it bounced.

Answer 3

Impossible to calculate without the physical characteristics of the ball, elasticity etc.