Question

Can someone help me with this? A 2.0-kg cart and a 3.0-kg cart collide on a low-friction track. The 3.0-kg cart is initially moving at 1.5m/s to the right, but after the collision it is moving at 5.5m/s to the right. After the collision, the 2.0-kg cart is moving to the right at 3.0m/s. If the direction from left to right is positive, what was the 2.0-kg carts initial velocity?

Answer 1

Initial velocity of cart 1 = 9 m/s to the right

Explanation:

Here momentum is conserved.

Initial momentum = Final momentum.

Mass of cart 1, m₁ = 2 kg

Mass of cart 2, m₂ = 3 kg

Initial velocity of cart 2, v₂₁ = 1.5 m/s

Final velocity of cart 2, v₂₂ = 5.5 m/s

Final velocity of cart 1, v₁₂ = 3 m/s

We need to find initial velocity of cart 1, v₁₁

We have

m₁v₁₁ + m₂v₂₁ = m₁v₁₂ + m₂v₂₂

2 x v₁₁ + 3 x 1.5 = 2 x 3 + 3 x 5.5

2 x v₁₁ = 18

v₁₁ = 9 m/s

Initial velocity of cart 1 = 9 m/s to the right

Answer 2

This is an inelastic collision. Since the two cars stick together, both are moving to the right. It is a rear end collision of A into B. Using the conservation of momentum is enough to solve for one unknown variable.
m1v1 + m2v2 = Mvf
(2.0)(v1) + (3.0)(1.5) = (5.0)(5.5)
The initial velocity is 11.5 m/s.