How do quadratics, series, and sequences relate to a ball being dropped and bounced?

Question

I'm working on an algebra project and we haven't done this in so long and I am very lost. Any help would be appreciated.

Answer 1

With a bouncing ball, each bounce has height y as quadratic function in time y(t) or x if there is a constant x-velocity. The form in time is y(t)=v₀*t-4.9*t². The initial velocity in y-direction determines the height of each bounce.

If the bounce is perfectly elastic, then the ball will reach the same height each time. But if it loses the same fraction of kinetic energy each time to heat, then the height of the ball can be modeled as a geometric sequence. h=KEmax/(mg). If for example the ball loses 20% of kinetic energy in each bounce, then the geometric sequence can be expressed as h_n=h₀ *0.8ⁿ.