Three identical train cars, coupled together, are rolling east at speed v0. a fourth car traveling east at 2v0 catches up with the three and couples to make a four-car train. a moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train.

what is the speed of the five-car train?

express your answer in terms of v0

Explanation:

Assuming that cars 4 and 5 have same mass so that the momentum  

P=mv where m is mass and v is velocity hence

Momentum=0+2mv+3mv=5mv

The final mass is 2m+3m=5m

From aw of conservation of momentum

hence

Therefore, the speed is

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm