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August 30th, 2014, 12:40 AM   #1
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From: South Wales

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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
Chilli Bean is offline  
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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skipjack is offline  
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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