Question

A school bus has a mass (including the driver and passengers) of 1.64 times 10^4 kg and is driving north at a speed of 15.2 km/h. Another school bus whose empty mass is 1.578 times 10^4 kg is moving south at a speed of 12.2 km/h. Assuming an average passenger mass of 64.8 kg, what is the minimum number of passengers (including the driver) of the southbound bus so that the total momentum of the two buses is directed south?

Answer 1

Step-by-step explanation:

Given

mass of bus along with travelers travelling in North direction is
`m_1=1.6* 10^4 kg`

speed of bus towards North
`v_1=15.2 km/h\approx 4.22\ m/s`

mass of bus travelling in South direction is
`m_2=1.578* 10^4 kg`

speed of bus
`v_2=12.2 km/h\approx 3.38\ m/s`

mass of each Passenger in south moving bus
`m_0=64.8 kg`

Momentum of North moving bus

`P_1=m_1* v_1`

`P_1=1.6* 10^4* 4.22`

`P_1=6.768* 10^4 kg-m/s`

Momentum with south moving bus

`P_2=m_2* v_2+n\cdot m_0* v_2`

`P_2=(1.578* 10^4+n\cdot 64.8 )\cdot 3.38`

For total momentum to be towards south

`P_2-P_1` should be greater than 0

thus for least value of n

`P_2=P_1`

`(1.578* 10^4+n\cdot 64.8 )\cdot 3.38=6.768* 10^4`

`1.578* 10^4+n\cdot 64.8=2.0023* 10^4`

`n=(4243.6686)/(64.8)=65.48\approx 66`