Answer to Question #172913 in Physics for Margarette

Question

A school bus carrying 20 students has a mass of 2500 kg and moves with a speed of 4.25 m/s. The driver has a mass of 75.0 kg.

(a)   What is magnitude of the momentum of the bus and its passenger if the average mass each student is 125kg?

(b)  If eight student get off from the bus, what must be the speed of the bus to maintain its origin momentum?

Answer 1

(a) The magnitude of the momentum of the bus and its passenger if the average mass of each student is 125kg:

$$p=p_\text{bus}+p_\text{stu}=m_\text{bus}v+m_\text{stu}v=\\ =2500·4.25+125·4.25=11160\text{ kg-m/s}.$$

(b)  If eight student get off from the bus, to maintain its original momentum, the speed of the bus must be

$$u=\frac{p_\text{orig}}{m_\text{rest}}.\\\space\\ p_\text{orig}=vm_\text{orig}=4.25(75+20·125+2500)=\\=21570\text{ kg-m/s}. \\ m_\text{rest}=75+2500+(20-8)125=4075\text{ kg}.\\\space\\ u=\frac{p_\text{orig}}{m_\text{rest}}=\frac{21570}{4075}=5.3\text{ m/s}.$$