Un cazador escucha el eco de su tiro 5s después que dispara su rifle. La velocidad del sonido en el aire es 330m/s. La superficie que refleja el sonido se encuentra a una distancia igual a:​

1)    μ₁ = (1 + m₂/m₁ )/3  tan θ - m3/3m₁   scs θ , 2)   W₃ = g (m₁ + m₂) sin θ + 3f , 3) a₁ = g sin θ - f / m₁

Explanation:

For this problem we must use Newton's second law, as the speed of the blocks is constant zero acceleration

Let's look at the attachment for the names of the forces. Let's write the equations for each body

Body 3

     T- W₃ = 0

     T = W₃

Body 2

Y Axis

     N- Wy₂ = 0

     N = ₂

X axis

     Wₓ₂- T₃ + T₁ -fr₂ = 0

Let's use trigonometry to find the weight components

     sin θ = Wₓ₂ / W₂

    cos θ = ₂ / W₂

    Wₓ₂ = W₂ sin θ

    ₂ = W₂ cos θ

They indicate that the friction force of block 2 is

    fr₂ = 2f

We replace

    W₂ sin θ - T₃ + T₁ - 2f = 0

Body 1

Y Axis

     N₁ - ₁ = 0

X axis

     Wₓ₁ -T₁- fr₁ = 0

If we use the same trigonometry equation as for body 2

    Wₓ₁ = W₁ sin θ

    ₁ = W₁ cos θ

Give the rubbing force of block 1

   fr₁ = f

We replace

   W₁ sin θ - T₁ - f = 0

Let's write our system of equations

   T₃ - W₃ = 0

   W₂ sintea - T₃ + T₁ - 2f = 0

   W₁ sintea - T₁ - f = 0

Add the three equations

    W₂ sin θ + W₁ sin θ -W₃ - 3f = 0

    g sin θ (m₂ + m₁) - m₃ g = 3f

    f = g [(m₁ + m₂) sin θ - m₃] / 3

   The formula for friction force is

    fr₁ = μ N₁

    fr₁ = f = μ W₁ cos θ

    μ₁ = f / m₁ g cos θ

    μ₁ = g [(m₁ + m₂) sin θ - m₃] / 3 m₁ g cos θ

    μ₁ = (1 + m₂/m₁ )/3  tan θ - m3/3m₁   scs θ

2)  add 2 and 3 equation

    W₂ sin θ + W₁ sin θ - T₃ - 3f = 0

    T₃ = g (m₁ + m₂) sin θ + 3f

    W₃ = g (m₁ + m₂) sin θ + 3f

3) when cutting the rope T1 = 0

   W₁ sin θ - f = m₁ a₁

   a₁ = g sin θ - f / m₁