The answer is B. helium-filled balloon, since sound travels the slowest through gases.
Answer:
Explanation:
Given
mass of bus along with travelers travelling in North direction is ![m_1=1.6\times 10^4 kg](https://tex.z-dn.net/?f=m_1%3D1.6%5Ctimes%2010%5E4%20kg)
speed of bus towards North ![v_1=15.2 km/h\approx 4.22\ m/s](https://tex.z-dn.net/?f=v_1%3D15.2%20km%2Fh%5Capprox%204.22%5C%20m%2Fs)
mass of bus travelling in South direction is ![m_2=1.578\times 10^4 kg](https://tex.z-dn.net/?f=m_2%3D1.578%5Ctimes%2010%5E4%20kg)
speed of bus ![v_2=12.2 km/h\approx 3.38\ m/s](https://tex.z-dn.net/?f=v_2%3D12.2%20km%2Fh%5Capprox%203.38%5C%20m%2Fs)
mass of each Passenger in south moving bus ![m_0=64.8 kg](https://tex.z-dn.net/?f=m_0%3D64.8%20kg)
Momentum of North moving bus
![P_1=m_1\times v_1](https://tex.z-dn.net/?f=P_1%3Dm_1%5Ctimes%20v_1)
![P_1=1.6\times 10^4\times 4.22](https://tex.z-dn.net/?f=P_1%3D1.6%5Ctimes%2010%5E4%5Ctimes%204.22)
![P_1=6.768\times 10^4 kg-m/s](https://tex.z-dn.net/?f=P_1%3D6.768%5Ctimes%2010%5E4%20kg-m%2Fs)
Momentum with south moving bus
![P_2=m_2\times v_2+n\cdot m_0\times v_2](https://tex.z-dn.net/?f=P_2%3Dm_2%5Ctimes%20v_2%2Bn%5Ccdot%20m_0%5Ctimes%20v_2)
![P_2=(1.578\times 10^4+n\cdot 64.8 )\cdot 3.38](https://tex.z-dn.net/?f=P_2%3D%281.578%5Ctimes%2010%5E4%2Bn%5Ccdot%2064.8%20%29%5Ccdot%203.38)
For total momentum to be towards south
should be greater than 0
thus for least value of n
![P_2=P_1](https://tex.z-dn.net/?f=P_2%3DP_1)
![(1.578\times 10^4+n\cdot 64.8 )\cdot 3.38=6.768\times 10^4](https://tex.z-dn.net/?f=%281.578%5Ctimes%2010%5E4%2Bn%5Ccdot%2064.8%20%29%5Ccdot%203.38%3D6.768%5Ctimes%2010%5E4)
![1.578\times 10^4+n\cdot 64.8=2.0023\times 10^4](https://tex.z-dn.net/?f=1.578%5Ctimes%2010%5E4%2Bn%5Ccdot%2064.8%3D2.0023%5Ctimes%2010%5E4)
<u>Answer</u>
The combined displacement is 2km north
<u>Explanation</u>
Since displacement is a vector quantity, we take into account the direction.
Good for us all the displacement vectors are in the same dimension, so we can make north positive and south negative or vice-versa.
We now add to obtain,
![4+-2+5+-5](https://tex.z-dn.net/?f=4%2B-2%2B5%2B-5)
This will simplify to
![=4-2+5-5=2](https://tex.z-dn.net/?f=%3D4-2%2B5-5%3D2)
Therefore the combined displacement is 2km north