Question

a 2,000 kg truck is moving at 15 m/s and collides head - on with a 1,000 kg car initially at rest. if the collision is perfectly elastic, what is the velocity of the truck after the collision?
a. 20 m/s
b. 15 m/s
c. 10 m/s
d. 5 m/s

Explanation:

Step1: Write the formula for conservation of momentum

$$m_1u_1 + m_2u_2=m_1v_1 + m_2v_2$$
where \(m_1 = 2000\space kg\), \(u_1=15\space m/s\), \(m_2 = 1000\space kg\), \(u_2 = 0\space m/s\)

Step2: Write the formula for elastic collision (relative velocity)

$$u_1 - u_2=v_2 - v_1$$
Since \(u_2 = 0\), we have \(v_2=u_1 + v_1\)

Step3: Substitute \(v_2\) into the momentum equation

$$
LATEXBLOCK0
$$

Answer:

D. \(5\space m/s\)