A ball falls under gravity from a height of 10m with an initial downward velocity u . It loses three-fifths (or 60%) of its energy in collision and then rises back to 5m. The initial velocity u is ( g = 10 ms ⁻² )

Step-by-step solution

Let the mass of the ball be m Initial total energy of the ball at height h₁ = 10 is E_i = mgh₁ + 1 2 mu^2 E_i = m(10)(10) + 0.5mu^2 = 100m + 0.5mu^2 The ball loses 60 % of its energy upon collision, so the remaining energy is 0.4E_i The ball rises to a height h₂ = 5 , so the final energy at the highest point is E_f = mgh₂ = m(10)(5) = 50m Equating the remaining energy to the final energy gives 0.4(100m + 0.5mu^2) = 50m 40m + 0.2mu^2 = 50m 0.2u^2 = 10 u^2 = 50 u = 50 7.07 ms⁻¹