Question

A 20-kilogram cart traveling east with a speed of 6 meters per second collides with a 30- kilogram cart traveling west. If both carts come to rest immediately after the collision, what was the speed of the westbound cart before the collision ?

Answer 1

The speed of the westbound cart before the collision is 4 m/s.

The given parameters:

• Mass of the first cart, m₁ = 20 kg
• Mass of the second cart, m₂ = 30 kg
• Initial velocity of the first cart, u₁ = 6 m/s.
• Initial velocity of the second cart, u₂ = ?

Conservation of linear momentum

The initial velocity of the second cart is determined by applying the principle of conservation of linear momentum.

$m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\ 20(6) + 30(-u_2) = 0(20 + 30)\\\\ 120 - 30u_2 = 0\\\\ 30u_2 =120\\\\ u_2 =\frac{120}{30} \\\\ u_2 = 4 \ m/s$

Thus, the speed of the westbound cart before the collision is 4 m/s.

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