A3.5 kg block slides along a frictionless horizontal with a speed of 2.5 m/s. after sliding a distance of 5 m, the block makes a smooth transition to a frictionless ramp inclined at an angle of 50â—¦ to the horizontal. the acceleration of gravity is 9.81 m/s 2 .

  L = 0.416 m

Explanation:

In this exercise to calculate the distance traveled in the branch that climbs the block we can use the concepts of energy

Starting point Flat part

       Em₀ = K = ½ m v²

Final point. Highest part of the ramp

        = U = m g h

As there is no friction the mechanical energy is conserved

        Em₀ =  

        ½ m v² = m g h

       h = v² / 2g

       h = 2.5 2/2 9.8

       h = 0.3189 m

The distance traveled can be found with trigonometry

      sin 50 = h / L

      L = h / sin 50

      L = 0.3189 / sin50

      L = 0.416 m