1. a 2000-kg car traveling at 20 m/s collides with a 1000-kg car at rest at a stop sign. if the 2000-kg car…

1. a 2000-kg car traveling at 20 m/s collides with a 1000-kg car at rest at a stop sign. if the 2000-kg car has a velocity of 6.67 m/s after the collision, find the velocity of the 1000-kg car after the collision.

1. a 2000-kg car traveling at 20 m/s collides with a 1000-kg car at rest at a stop sign. if the 2000-kg car has a velocity of 6.67 m/s after the collision, find the velocity of the 1000-kg car after the collision.

Answer

Explanation:

Step1: Apply conservation of momentum

Momentum before collision = Momentum after collision: $$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$$ Where $m_1=2000\ \text{kg}$, $v_{1i}=20\ \text{m/s}$, $m_2=1000\ \text{kg}$, $v_{2i}=0\ \text{m/s}$, $v_{1f}=6.67\ \text{m/s}$

Step2: Substitute known values

$$(2000)(20) + (1000)(0) = (2000)(6.67) + (1000)v_{2f}$$ $$40000 = 13340 + 1000v_{2f}$$

Step3: Solve for $v_{2f}$

$$1000v_{2f} = 40000 - 13340$$ $$1000v_{2f} = 26660$$ $$v_{2f} = \frac{26660}{1000} = 26.66\ \text{m/s}$$

Answer:

$\boldsymbol{26.66\ \text{m/s}}$