Obviously (I think!) one lap of a standard athletics track is only 400m when you are in lane 1, the inside lane, how much further do you travel when doing a lap in lanes 2, 3, 4 etc., one lap being from the main start/finish line back to the main start/finish line i.e. without staggered starts?
2006-07-07 23:50:59 · 12 answers · asked by quanto_questo 1 in Science & Mathematics ➔ Mathematics
The length of lane n is 400m + (n-1)*(2*pi*w), where w is the lane width. The shape of the track doesn't matter, as long as it is convex (i.e., lanes only turn left, never right).
2006-07-08 01:35:09 · answer #1 · answered by ernie cohen 1 · 0⤊ 0⤋
The easiest way is to find out how far the staggered start is between lane 1 and lane 2. Suppose this is y metres
Lane 2 would be 400 + y metres
Lane 3 would be 400 + 2y metres
Lane n would be 400 + (n-1)y metres
2006-07-09 10:48:12 · answer #2 · answered by Anonymous · 0⤊ 0⤋
If you look at a athletics track it consists of 4 parts, 2 of them are straight lines, and 2 are circle half's. If you connect the 2 circle half's you will get a whole circle. Difference between lane 1 and lane 2 is that lane 2 has a "bigger" circle then lane 1. The straight lines remain the same at each lane. Length of the circle in lane 1 is 2*radius*pi. Length of the circle in lane 2 is 2*(radius+lane width)*pi. Radius of the circle in lane 1 is 400m minus the 2 straight lines, and divided by 2*pi.
All you need is the length of those straight parts(lines).
2006-07-08 00:56:59 · answer #3 · answered by madnaco 1 · 0⤊ 0⤋
assuming that each lane is 1 metre wide then each extra lane would add about 6 metres to the length - so lane 3 would actually be around 412 metres
this is why they have staggered starts
2006-07-08 00:05:50 · answer #4 · answered by Ivanhoe Fats 6 · 0⤊ 0⤋
hmmm... lanes.. tracks.. first of all.. it depends upon how wide the lanes are made... and the distance across the infield of the track.
but.. let's break this down into smaller bits...
for the straight-away... the lengths are the same in all lanes.. so we only need to consider the curves... but how long is the straight portion? is it 100m?
the curve on each end is a semi-circle with a diameter the size of the infield, so you have a full circle distance total, with the two ends.
so, for lane 1, you have 2(length of straightaway) + 2pi(width of infield) = 400m.
for lane 2, you have 2(length) + 2pi[width + (width of lane 1)] = ?
but you only need the difference.. so Lane 2 - Lane 1
[2(length) + 2pi(width) + 2pi (lane width)] - [2(length) + 2pi(width)]
or..
2(length)-2(length) + 2pi(width)-2pi(width) + 2pi(lane width)
or..
0 + 0 + 2pi(lane width)
so each lane increases by 2pi(lane width) in distance.
oh.. just read ernie's answer.. much simpler to understand.. oh well
2006-07-08 02:46:35 · answer #5 · answered by ♥Tom♥ 6 · 0⤊ 0⤋
Its clearly not the same , otherwise it wouldn't be a staggered start.
If it was the same people would be running in the outside lane in the 1500m, the question was WITHOUT the staggered start.
I dont know, its a mathamatical question, and too complicated for me.
2006-07-07 23:59:36 · answer #6 · answered by Anonymous · 0⤊ 0⤋
400m because the main start line is staggered, not a straight line, so you can't help but have a staggered start.
2006-07-07 23:57:06 · answer #7 · answered by charleymac 4 · 0⤊ 0⤋
Clearly it's not the same!!!
You would need to know the width of each lane I suppose.
2006-07-08 00:04:16 · answer #8 · answered by Apollo 2 · 0⤊ 0⤋
It would proberly measure the same for all lanes.
2006-07-07 23:55:42 · answer #9 · answered by fantasy_gamer_uk 2 · 0⤊ 0⤋
the same, 400m, thats why when they start, its not at the same line/pt
2006-07-07 23:55:09 · answer #10 · answered by leocorn1 2 · 0⤊ 0⤋