Question

two cars are involved in a head - on collision in an alley. the driver of a car with mass, ma = 1,200 kg claims to have been traveling west at via = 7 m/s. the driver of the other car with mass, mb = 1,000 kg claims to have been traveling east at vib = 10 m/s. the investigating officer found that both cars were stuck together and traveled with a common final velocity after the collision. which direction would they be moving after the collision? options: west, east, north, no direction/ not moving

Explanation:

Step1: Define Momentum Directions

Assign east as positive and west as negative. For car \( a \) (mass \( m_a = 1200 \, \text{kg} \), velocity \( v_{ia} = -7 \, \text{m/s} \) (west)), momentum \( p_a = m_a v_{ia} \). For car \( b \) (mass \( m_b = 1000 \, \text{kg} \), velocity \( v_{ib} = 10 \, \text{m/s} \) (east)), momentum \( p_b = m_b v_{ib} \).

Step2: Calculate Initial Momenta

Calculate \( p_a \): \( p_a = 1200 \times (-7) = -8400 \, \text{kg·m/s} \). Calculate \( p_b \): \( p_b = 1000 \times 10 = 10000 \, \text{kg·m/s} \).

Step3: Total Initial Momentum

Total initial momentum \( p_{\text{total}} = p_a + p_b = -8400 + 10000 = 1600 \, \text{kg·m/s} \).

Step4: Analyze Final Direction

Since total momentum is positive (east direction, as east is positive), the combined cars will move in the direction of the positive momentum, which is east.

Answer:

east (corresponding to the option "east")