An 81-kg physicist and a friend are ice-skating. The physicist, distracted, collides from behind at 7.0 m/s with his friend, who is skating at 5.0 m/s in the same direction. After the collision, the physicist continues in the same direction at 4.0 m/s, but his friend is now moving (still in the same direction) at 8.0 m/s. What is her inertia?

The inertia of an object is its resistance to linear acceleration due to an applied force-that is to say, the inertia of the physicist's friend is her mass.

Apply the conservation of linear momentum for the situation wherein two colliding objects separate after the collision:

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Let us choose m₁ to be the mass of the physicist. v₁ and v₁' are velocities of the physicist before and after the collision, respectively.

m₂ is the mass of the physicist's friend. v₂ and v₂' are the velocities of the friend before and after the collision, respectively.

Given values:

m₁ = 81kg

v₁ = 7.0m/s

v₁' = 4.0m/s

v₂ = 5.0m/s

v₂' = 8.0m/s

Plug in the given values and solve for m₂

81*7.0 + 5.0m₂ = 81*4.0 + 8.0m₂

3.0m₂ = 243

m₂ = 81kg