You are on an RTD Stretch Bus (the long busses with the accordionin the middle.

Question

You are on an RTD Stretch Bus (the long busses with the accordionin
the middle. (This is called an articulating bus.)) The bus isfully
loaded with fuel and people. You are traveling at 30 [mph] whena
mini-Van in front of the bus pulls in front of the bus as ittravels in
a similar direction; the van is traveling 20 [mph]. The bus driverslams
on the brakes, but there is black ice so the bus gracefullyslides
right into the van sending the van flying ahead. Threepassengers,
upon realizing their opportunity to make some quick cash, startcrying
of back and neck pain.

Mass of bus + passengers + fuel is about 66,600 [lb] or 30,200[kg].
Mass of van is about 2,000 [kg].

Forensics estimates from the bending of the light-pole that the vanwas
moving at an uninhibited speed of about 35 [mph] when it hit thepole
after sliding on ice.

You are a professional witness; what is your statement tothe judge
and why? (Three other passengers tell the judge they didn't evenfeel
the collision. They heard it and saw the van fly forward; butthey
claim they felt nothing.)

Explanation / Answer

Here we must find the final velocity of the bus , Let it be V Then final momentum of bus = 30200V Final momentum of van after collision = 2000*35 Total final momentum = 30200V + 70000 Initial momentum of bus = 30200*30 Initial momentum of van =2000*20 So total initial momentum = 40000+906000 From law of conservation of momentum , Initial momentum = final momentum SO 40000+906000 = 30200V +70000 30200V = 876000 V = 29 So final velocity of bus = 29 mph Here the change in velocity is only 1 mph , So there is no probability of any serious injuries .

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