TP 8.26

Initially:

E_i = K_1i + K_2i + U_g1i + U_g2i  = 1/2 m₁v_1i² + 1/2 m₂v_2i² + m₁g y_1i+ m₂g y_2i   = 0 + 0 + 0 + 0 = 0

Just before mass m₂ lands:

E_f = K_1f + K_2f + U_g1f + U_g2f  = 1/2 m₁v_f² + 1/2 m₂v_f² + m₁g y_1f+ m₂g y_2f   = 1/2 m₁v² + 1/2 m₂v² +  m₁g h + m₂g (- h)  

Assuming that friction can be ignored, E_i = E_f :

1/2 m₁v² + 1/2 m₂v² +  m₁g h + m₂g (- h)   = 0

1/2 v²( m₁+ m₂) = -  m₁g h -  m₂g (- h)

1/2 v²( m₁+ m₂) = g h ( m₂ - m₁)

v²( m₁+ m₂) = 2 g h ( m₂ - m₁)

v² = 2 g h ( m₂ - m₁)/( m₁+ m₂)

v = (2 g h ( m₂ - m₁)/( m₁+ m₂))^1/2

v = (2 (9.81 m/s²) (1.20 m)( 4.10 kg - 3.70 kg)/( 4.10 kg+ 3.70 kg))^1/2

v = 1.10 m/s