Respuesta :
Answer:
y = 54.9 m
Explanation:
For this exercise we can use the relationship between the work of the friction force and mechanical energy.
Let's look for work
   W = -fr d
The negative sign is because Lafourcade rubs always opposes the movement
On the inclined part, of Newton's second law
Y Axis Â
   N - W cos θ  = 0
The equation for the force of friction is
   fr = μ N
   fr = μ mg cos θ
We replace at work
   W = - μ m g cos θ  d
Mechanical energy in the lower part of the embankment
   Em₀ = K = ½ m v²
The mechanical energy in the highest part, where it stopped
   [tex]Em_{f}[/tex] = U = m g y
   W = ΔEm =  [tex]Em_{f}[/tex] - Em₀
  - μ m g d cos θ = m g y - ½ m v²
Distance d and height (y) are related by trigonometry
   sin θ = y / d
   y = d sin θ
 Â
  - μ m g d cos θ = m g d sin θ - ½ m v²
We calculate the distance traveled
   d (g syn θ + μ g cos θ) = ½ v²
   d = v²/2 g (sintea + myy cos tee)
   d = 9.8 12.6 2/2 9.8 (sin16 + 0.128 cos 16)
   d = 1555.85 /7.8145
   d = 199.1 m
Let's use trigonometry to find the height
   sin 16 = y / d
   y = d sin 16
   y = 199.1 sin 16
   y = 54.9 m
