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A car moving with an initial speed v collides with a second stationary car that is...

A car moving with an initial speed v collides with a second stationary car that is 55.0 percent as massive. After the collision the first car moves in the same direction as before with a speed that is 34.6 percent of the original speed. Calculate the final speed of the second car. Give your answer in units of the initial speed (i.e. as a fraction of v). Is this collision elastic or inelastic? The collision is inelastic. The collision is elastic.

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Answer #1

Let M be the mass of the car amcd v be the initial mass of the car

The mass of the second car is 0.55M

The final speed of the firct car is 0.346v

Let v' be the speed of the second car

According to the conservation of linear momentum

Mv = M*0.346v + 0.55M*v'

v' = 0.896v

Therefore the final speed of the second car is 0.896 times the initial speed of the first car  

The initial kinetic energy of the system Ki = 0.5Mv2

The final kinetic energy of the system is Kf = 0.5*M(0.346)2 + 0.5(0.55M)(0.896v)2

Kf = 0.28*Mv2

The kinetic energy of the system is not conserved during the collision

Therefore the collision is inelastic in nature

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