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August 30th, 2014, 12:40 AM   #1
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Can You Help Me Solve A Traffic Incident Using Math?

Hi, I'm trying to verify some calculations relating to a road traffic incident and need some help to make sure my results are accurate. Here's the problem:

A red car is approaching a bend at 50 miles/hour. A blue car starts to overtake the red car prior to the bend at 65 miles/hour. During this overtake manoeuvre there is a collision between the blue car and a white car travelling in the opposite direction. The collision happened just one car's length ahead of the red car. The red car is 4 metres long, so the collision happened another 4 metres ahead of the red car. No braking occurred during the incident, so the estimated speeds are constant.

Question: approximately how far had the blue car travelled, in metres, between the start of the overtake manoeuvre and the collision with the white car?

Thanks for your help in advance
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August 31st, 2014, 02:47 PM   #2
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Suppose the overtaking car needs to travel 8m to overtake a car at rest.
Multiply that distance by 65/(65 - 50).
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September 2nd, 2014, 01:13 PM   #3
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Hi, thanks for your reply. Yes, I did something similar to that. Firstly I converted the miles/hour figures into metres/hour (1 mile = 1609.34 metres) and then I calculated how long it would take to cover 10 metres to overtake a car at rest (10 metres because I have to take into account the length of the overtaking vehicle, which is just 2 metres because it's actually a motorcycle not a car - didn't think I'd need to mention that at first). So for a 2 metre motorcycle to be a car's length ahead would mean that the front end would have to be six metres ahead of the front end of the car, giving a total of 10 metres. Then I multiplied the time it would take to cover 10 metres (1.49 seconds) by the metres/second speed of the motorcycle (29.05), which gave 43.28. Sounds like your method is an easier method though.

I hope my calculations are correct as I need them for a court case. Using your method I get 43.33 but using my method I get 43.28? I mean, it won't make much difference to the outcome but I'd rather have my calculations as accurate as possible.
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