select the correct answer.\na bus and a car have an inelastic head - on collision. the bus has a mass of…

Explanation:

Step1: Recall the law of conservation of momentum

In an in - elastic collision, the total momentum before the collision is equal to the total momentum after the collision. The formula for momentum is $p = mv$, and the total initial momentum $p_{total}=m_1v_1 + m_2v_2$.

Step2: Identify the values of mass and velocity

Let $m_1 = 1.5\times10^{3}\text{ kg}$, $v_1=+ 20\text{ m/s}$, $m_2 = 9.5\times10^{2}\text{ kg}$, and $v_2=-26\text{ m/s}$.

Step3: Calculate the total initial momentum

[ \begin{align*} p_{total}&=m_1v_1 + m_2v_2\ &=(1.5\times 10^{3}\text{ kg})\times(20\text{ m/s})+(9.5\times 10^{2}\text{ kg})\times(- 26\text{ m/s})\ &=(1.5\times10^{3}\times20)\text{ kg}\cdot\text{m/s}-(9.5\times10^{2}\times26)\text{ kg}\cdot\text{m/s}\ &=30\times10^{3}\text{ kg}\cdot\text{m/s}-24.7\times10^{3}\text{ kg}\cdot\text{m/s}\ &=(30 - 24.7)\times10^{3}\text{ kg}\cdot\text{m/s}\ &=5.3\times10^{3}\text{ kg}\cdot\text{m/s} \end{align*} ]

Answer:

C. $5.3\times 10^{3}$ kilogram meters/second