And 84.1 kg man is standing on a frictionless ice surface when he throws a 1.80 kg book at 11.1 m/s. With what velocity does the man move across the ice

Final velocity of man is - 0.23 m/s.

Explanation:

Conservation of linear momentum:

When no external force acts on a system of several interacting particles, the total linear momentum of system is conserved.

Before the Throw; Man mass (M₁) = 84.1 kg,

Velocity of Man (u₁) = 0 m/s

Book Mass (M₂) = 1.80 kg

Velocity of book (u₂) = 0 m/s

After the throw; Man mass (M₁) = 84.1 kg

Velocity of Man (V₁) = ?

Book mass (M₂) = 1.80 kg

velocity of book (V₂) = 11.1 m/s

According to conservation of linear Momentum

Initial Momentum = Final Momentum

M₁u₁ + M₂u₂ = M₁v₁ + M₂v₂

84.1 x0 + 1.80 x0 = 84.1 x v₁ + 1.80 x 11.1

0 = 84.1 v₁ + 19.98

v₁ = - 19.98 / 84.1

= - 0.23 m/s

final velocity of man is - 0.23 m/s