# The cart moves at a speed of 3m / s and collides with the second cart, which is stationary.

**The cart moves at a speed of 3m / s and collides with the second cart, which is stationary. After the collision, the first trolley rolls back at a speed of 1.5 m / s, and the second begins to move at a speed of 0.5 m / s. Determine the mass of the second cart if the mass of the first is 1 kg.**

To find the mass of the second bogie, we will use the equality (the law of conservation of momentum, we consider the initial velocity vector of the first given bogie to be the positive direction): mt1 * Vt1 = mt2 * Ut2 – mt1 * Ut1, whence we express: mt2 = (mt1 * Vt1 + mt1 * Ut1 ) / Uт2.

Variables: mt1 is the mass of the first given bogie (mt1 = 1 kg); Vt1 – initial speed of the first carriage (Vt1 = 3 m / s); Uт1 – speed after the collision of the first bogie (Uт1 = 1.5 m / s); Ut2 – speed after collision of the second carriage (Ut2 = 0.5 m / s).

Calculation: m2 = (1 * 3 + 1 * 1.5) / 0.5 = 9 kg.

Answer: The mass of the second cart is 9 kg.