Question

question 8. a 3,000 kg car is moving at 20 m/s and collides with a 1,500 kg car that is initially at rest. what is the final velocity of the two cars if the collision is perfectly inelastic (they stick together)? a. 13 m/s b. 33 m/s c. 49 m/s d. 62 m/s

Explanation:

Step1: Apply the law of conservation of momentum

The formula for conservation of momentum in a perfectly inelastic collision is \(m_1v_1 + m_2v_2=(m_1 + m_2)v_f\). Here, \(m_1 = 3000\space kg\), \(v_1=20\space m/s\), \(m_2 = 1500\space kg\), and \(v_2 = 0\space m/s\) (since the second car is initially at rest).
Substituting the values into the formula: \(3000\times20+1500\times0=(3000 + 1500)v_f\)

Step2: Solve for \(v_f\)

First, simplify the left - hand side of the equation: \(3000\times20+1500\times0 = 60000+0=60000\)
The right - hand side is \(4500v_f\) (because \(3000 + 1500=4500\)).
So, \(4500v_f=60000\). Then \(v_f=\frac{60000}{4500}=\frac{40}{3}\approx13.33\space m/s\)

Answer:

A. \(13\space m/s\)