Question

a rail car moving at 10 m/s collides with and connects to another stationary car. what is their final velocity? assume they have the same mass. select one answer a -10 m/s b 0 m/s c 5 m/s d 10 m/s

Explanation:

Step1: Recall Conservation of Momentum

The law of conservation of momentum states that the total momentum before a collision equals the total momentum after the collision, i.e., \( m_1v_1 + m_2v_2 = (m_1 + m_2)v_f \) where \( m_1, m_2 \) are masses, \( v_1, v_2 \) are initial velocities, and \( v_f \) is the final velocity.

Step2: Define Variables

Let the mass of each rail car be \( m \). The first car has \( v_1 = 10 \, \text{m/s} \), the second car (stationary) has \( v_2 = 0 \, \text{m/s} \), and after collision, their combined mass is \( m + m = 2m \).

Step3: Apply Momentum Conservation

Substitute into the formula: \( m(10) + m(0) = (m + m)v_f \). Simplify left side: \( 10m \). Right side: \( 2m v_f \). Divide both sides by \( 2m \) ( \( m
eq 0 \) ), so \( v_f = \frac{10m}{2m} = 5 \, \text{m/s} \).

Answer:

C. 5 m/s