one way street

Question

one way street

perl · Answer

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anonymous · Answer

On a one-way street, an unending sequence of cars of width a,
length b passes with velocity v. The cars are separated by the distance c.
A pedestrian crosses the street perpendicularly with velocity w, without
paying attention to the cars.
a)What is the probability that the pedestrian crosses the street uninjured?
b)Can he improve this probability by crossing the road in a direction
other than perpendicular?

anonymous · Answer

ne diyon la sen??

jamesj · Answer

Nice problem. Where are you so far in your thinking?

anonymous · Answer

no idea

anonymous · Answer

@mukushla @ParthKohli @hartnn @JamesJ @Hero@mathslover @experimentX @UnkleRhaukus  and everyone

anonymous · Answer

IMO LONGLIST 1985 PROBLEM 6
BELGIUM

anonymous · Answer

ALSO IF YOU CAN FIND THE SOLUTION FROM ANY WEBSITE

jamesj · Answer

Well, for a portion a wide of the street, one of the cars is present or not. If it is present, the pedestrian is hit.

So calculate first of all the probability for time t = infinity how much of the time is the car present. 

What happens now if t is finite?

In short, you want to find a function P(t) where P(t) is the probability a car is present during a time period t long.

Then you need to find the time T that the pedestrian is in the street; the final answer then is P(T).

jamesj · Answer

Looking up is cheating. Figure it out from first principles. Much more fun.

anonymous · Answer

sounds like a good approach i;ll try it,and also have fun i hope all you guys can share this fun by @JamesJ

anonymous · Answer

first principles ???is that like instinct

jamesj · Answer

No, it means thinking through the problem systematically.

anonymous · Answer

okay i am on it,thanks

jamesj · Answer

Actually, better to define P(t) to be the probability that a car crosses a line perpendicular to the road for a given time period of length t.  Clearly P(infinity) = 1 for any speed of the cars, v, which is not zero.