Oh for goodness’ sake; the Red car will obviously stop much better than the Blue one because as we all know a Red car is a Sports Car, driven (always) by expert drivers that know how to get the very best performance out of their superior vehicles.
Not to mention that the driver of the self-evidently inferior Blue car will be looking enviously out of their window that the clearlt superior Red car and thus completely miss the tree being there.
Result; Blue goes Boom, Red is at Rest.
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If anyone wants a TLDR, here’s my try.
We use the kinematics equation VF2 = 2AS + V02
where VF is final velocity, V0 is initial velocity, A is acceleration, S is distance.
The first car decelerates (A) from 70 (V0) to 0 (VF) in distance S, so 02 = 2AS + 702
We dont know what the distance (S) is, nor do we know what the rate of deceleration (A) is. We dont need to know. All we need to know is 2AS = -702
The second car decelerates (A) from 100 (V0) to VF in same distance S, so VF2 = 2AS + 1002 = -702 + 1002
VF = √(-702 + 1002) = √5100 = 71.4
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That’s also true, but it leads to the same result, because the faster car has less time before it hits the tree to slow down.
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I see people do this at stop lights and I don’t really have a problem with it…except when there is now 3 cars behind them and an empty place for two cars in front. Come on, once a couple of cars roll up behind ease that space up.
I get the math and everything else, but there are a lot of real world assumptions here as well. Like the other driver decided to install something other than the cheapest brakes and most basic tires they could find. I typically gauge the other cars around me and what they are capable of in relation to what I’m driving. If the car in front of me is significantly better equipped then I’m going to leave enough room just in case.
the feedback loop unfortunately is too long to matter much.
most of the time, people are able to consider that their several near misses are because they are great drivers, not because they are terrible drivers. by the time the realization might sink in – it’s way too late.
my take is – and it always pisses the people i know off – is that everyone is a terrible driver. myself included. monkeys really don’t do well under stressful conditions at 70mph. no matter who they are.
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This takes me back pleasantly to the late 90s, when web design was the Wild West and I came across a great text-based HTML editor called Arachnophilia. They were restless times, so I moved on eventually, but I made good use of it for several months.
Anyhoo, the author, Paul Lutus, had a beautiful example of a pre-millennial personal website, covering all manner of topics, and I’d regularly dive in when I had time to spare. Definitely Happy Mutant stuff. The site’s still there, still updated (as is the software), including a demonstration of this very phenomenon: https://arachnoid.com/lutusp/auto.html.
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Not clicking on the video and not reading anybody’s answers, I get sqrt(100² - 70²) . amirite?
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What you (and others) seem to be missing is that the 100mph car will impact the tree before the 70mph car comes to a stop. How much will the impact displace the tree? Then recalculate the 70 mph solution, use that value to re-estimate the 100mph tree impact displacement and iterate a few more times until the solution converges sufficiently.
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How far is from reality to assume the braking deceleration to be constant?
This is better than the video, at least for me; thanks!
Ah, I know this one - the 70mph car will never reach the tree because by the time the car reaches where the tree was, it’s already moved a bit!
Xeno’s paradox, innit.
I do a basic form of quantity surveying on monotonous highway drives: whenever I pass a sign telling me the distance to a given town, I try to work out what time I’ll pass that town.
Recreational mathematics is a standard way to pass the time on long motorcycle trips. Converting your speed into furlongs per fortnight was always a favourite.
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If there’s restricted space for stopped cars, sure, don’t hog it. If it’s just a big straight lane with stopped cars though, as it often is, who cares? I’m mystified by people who edge their cars forward in stopped traffic. What’s the point?
You’re thinking of Zeno here. Xeno’s paradox stipulates that by the time the car reached the tree, it would already be empty, most of its passengers having been brutally murdered, except for one person and a cat who’d have gotten away in an escape pod.
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