On a low-friction track, a 0.81 kg cart initially going at 1.85 m/s to the right

The mass of unknown inertia is 0.476 kg.    

Explanation:

It is given that,

Mass of the cart, m₁ = 0.81 kg

Initial speed of cart, u₁ = 1.85 m/s (in right)

Initial speed of the other object, u₂ = -2.17 m/s (in left)

After the collision,

Final speed of the cart, v₁ = -1.32 m/s (in left)

Final speed of the other object, v₂ = 3.22 m/s (in right)

Let m₂ is the mass of the unknown inertia. Using the conservation of linear momentum to find the mass of unknown inertia.  

So, the mass of the unknown inertia is 0.476 kg. Hence, this is the required solution.

Final Answer

a.340 km/h

b.1.1×104 rev/min

is the correct answer