The three inclines have the same height and they are all frictionless, but they have different angles. Which object will have the highest speed at the bottom of the incline

the speed of the body must be the same for the three hills regardless of their slope

             v =

Explanation:

To shorten the answer to this exercise, let's use the concept of conservation of energy

starting point. Highest point of the hill

         Em₀ = U = m h y

final point. Lower part of the hill

         Em_f = K = ½ m v²

as there is no friction the mechanical energy is conserved

         Em₀ = Em_f

         mg y = ½ m v²

         v =

Let's analyze this result, we see that the speed at the bottom of the hill depends only on the height of the hill, not on the slope, so the speed of the body must be the same for the three hills regardless of their slope

see earlier