Question

7 a trolley of mass 4.0kg travelling with a velocity of 4.0m/s collides with a trolley of mass 2.0kg travelling with a velocity of 2.0m/s in the same direction. after the collision, the velocity of the 4.0kg trolley is reduced to 3.0m/s. what is the velocity v of the 2.0kg trolley after the collision? a 0.25m/s b 4.0m/s c 5.0m/s d 16m/s

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. The formula for momentum is \(p = mv\).
The total momentum before the collision \(p_{before}=m_1u_1 + m_2u_2\), where \(m_1 = 4.0\space kg\), \(u_1=4.0\space m/s\), \(m_2 = 2.0\space kg\), \(u_2 = 2.0\space m/s\).
So, \(p_{before}=4.0\times4.0+2.0\times2.0\)
\(p_{before}=16 + 4=20\space kg\cdot m/s\)

Step2: Calculate the total momentum after the collision

The total momentum after the collision \(p_{after}=m_1v_1 + m_2v_2\), where \(m_1 = 4.0\space kg\), \(v_1 = 3.0\space m/s\), \(m_2 = 2.0\space kg\), \(v_2=v\) (the velocity we want to find)
\(p_{after}=4.0\times3.0+2.0\times v\)
\(p_{after}=12 + 2v\)

Step3: Equate \(p_{before}\) and \(p_{after}\)

Since \(p_{before}=p_{after}\), we have the equation \(20=12 + 2v\)
Subtract 12 from both sides: \(20-12=2v\)
\(8 = 2v\)
Divide both sides by 2: \(v=\frac{8}{2}=4.0\space m/s\)

Answer:

B. \(4.0\space m/s\)