Use the energy relation mgh = (1/2)mv². Divide out mass, m to get
gh = v²/2 or v = √2gh
This relates the gravitational potential energy (GPE) to the kinetic energy (KE). If the ball is 85 meters up, that's h. g is 9.81m/s² (access due to gravity)
v= 40.84m/s
Its time to hit the ground can be found by integrating the acceleration twice to get the vertical position function: y = (9.81/2)·t². Since y must equal 85:
85=(9.81/2)·t² ; 17.33 = t² ; t = √17.33 = 4.16s
