Solve problems involving momentum, impulse, the conservation of momentum and collisions in one dimension using 𝑝 = 𝑚𝑣 and ∑ 𝑚𝑣𝑏𝑒𝑓𝑜𝑟𝑒 = ∑ 𝑚𝑣𝑎𝑓𝑡𝑒𝑟.

A trolley of mass 1.2 kg moving at 3.0 m s⁻¹ collides with a stationary trolley of mass 0.80 kg. After the collision, both trolleys move together. State the principle that allows the final velocity to be determined, and identify the combined momentum immediately after collision.

A railway shunting yard uses momentum principles to couple freight cars. Car A (mass 18,000 kg) rolls at 2.5 m s⁻¹ along a straight track and collides with stationary car B (mass 22,000 kg). After coupling, the joined cars move together at 1.125 m s⁻¹. A second identical coupling occurs on an adjacent track: car C (mass 18,000 kg) at 3.0 m s⁻¹ collides with stationary car D (mass 14,000 kg), and they move together at 1.688 m s⁻¹ after coupling. a) Justify whether momentum is conserved in the coupling of cars A and B. b) Predict, with reference to the data from both couplings, which scenario involves the greater percentage loss of kinetic energy. Explain your reasoning.

Calculate the velocity of the 2.5 kg trolley immediately after the collision.

A student investigates collisions between two trolleys on a horizontal track. Before the collision, trolley A (mass 0.50 kg) moves at 2.4 m s⁻¹ and trolley B (mass 0.30 kg) is stationary. After the collision, trolley A moves at 0.8 m s⁻¹ in the same direction. Compare the momentum of trolley B after the collision with the initial momentum of trolley A.