Question

question 18
a 1000 - kg car traveling east at 20 m/s collides with a 1500 kg car traveling west at 10 m/s. the cars stick together after the collision. what is the common velocity of the cars after the collision?
hint: see example 5 on page 179 of textbook
assign vector directions

• east
• west

○ 2 m/s, east
○ 16 m/s, east
○ 6 m/s, west
○ 1 m/s, west
○ 4 m/s, east

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(m_1v_1 + m_2v_2=(m_1 + m_2)v\). Let the east - ward direction be positive. So, \(m_1 = 1000\space kg\), \(v_1=20\space m/s\), \(m_2 = 1500\space kg\), \(v_2=- 10\space m/s\) (negative because it is moving west).

$$1000\times20+1500\times(-10)=(1000 + 1500)v$$

Step2: Simplify the left - hand side of the equation

$$20000-15000 = 2500v$$

$$5000=2500v$$

Step3: Solve for \(v\)

$$v=\frac{5000}{2500}=2\space m/s$$

Answer:

2 m/s, east