Question

Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide and how far? The coefficient of kinetic friction between football uniforms and the ground is 0.30.

Answer 1

Answer:

  x = 0.0756 m

Fred moves in the direction where Brutus moves

Explanation:

This exercise is for the moment, we define the system as formed by the two players, for this system the forces in the clash are internal, so the moment is preserved

Initial. Before the crash

       p₀ = m v₀₁ - M v₀₂

Final. After the crash

       $p_{f}$ = (m + M) v

       p₀ = $p_{f}$

       m v₀₁ –M v₀₂ = (m + M) v

       v = (m v₀₁ - M v₀₂) / (m + M)

Let's calculate

       v = (60 6 - 120 4) / (60 +120)

       v = - 120/180

       v = - 0.667 m / s

The negative sign indicates that the final speed is the direction where Brutus runs

Let's use Newton's second law to find the acceleration of the two players

       fr = (m + M) a

       fr = μ N

      N- W = 0

      N = (m + M) g

      μ (m + M) g = (m + M) a

      a = μ g

      a = 0.30 9.8

      a = 2.94 m / s²

We use kinematics to find the distance traveled, the final speed is zero

     v² = v₀² - 2 a x

     x = v₀² / 2 a

     x = 0.667² / (2 2.94)

     x = 0.0756 m