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