Jam Shock Speed

On a highway, there are 100 cars per kilometer and the cars are all moving at \(100 \text{ km/hr}\). One car notices something and slams on its breaks, slowing down to \(50 \text{ km/hr}\) and halving the distance between itself and the car behind it.

How quickly does the shock wave generated move relative to the ground (in\( \text{ km/hr}\))?

Give your answer to 3 decimal places.

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