Boats and a Buoy
Two boats, Knightmare's Couch and Chris's London Fog, leave the dock on a river simultaeously. Knightmare's Couch heads downstream, and Chris's London Fog upstream, both utilizing equal power. As they depart, a life bouy falls from Knightmare's Couch and floats with the river current. After an hour, both boats reverse course.
Which boat will reach the life bouy first?
Which boat will reach the life bouy first?
posted by Zaux at
6:41 PM
21 Comments:
Knightmare ... last time this dog will dig up this "couch" bone ... heh heh.
If the Fog is a boat, then it'll be a tie - regardless of the Fog's or Knightmare's couch's relative speeds as long as both speeds are > 0.
I bet Knightmare's couch is enjoying the attention and solving these problems.
Hi Pequod. You certainly have an adventurous life.
thanks Chris...i do enjoy my adventurous days and hope more to come.(but they would be better without this fat ass on me all day)
zaux-dig all u want
it's been good so far
london fog must have covered less distance since he was going upstream, its an hour voyage so at reverse course london was returning downstream(less resistance) and less distance therefore arriving first
... nooooooo. The Fog, Pequod and the buoy are all moving along with the river. So Pequod and the Fog's speed are with respect to the river, and hence with respect to the buoy. Completely ignore the river bank. Hence a tie.
It was a trick question.
of course it was knightmares couch as he was heading downstream and so was the buoy while the fog was heading upstream . by the time the hour was up the bouy would have been closer to knightmare as a river flows downstream
of course it was knightmares couch as he was heading downstream and so was the buoy while the fog was heading upstream . by the time the hour was up the bouy would have been closer to knightmare as a river flows downstream
Anonymous, try reading the question. The fog is just a joke. It is to be treated as a boat, and so it also is also being carried along with the river. Forget the real world.
... extreme case. If the fog and the couch didn't bother to move, then all three would remain together, forever.
if the bouy was stationary, it'd be a tie.... but it was moving closer to nightmare's couch, so nightmare's couch would be first...
*buoy*
Hi Anonymous. I'm finding it hard to work ou exactly what you were saying. Ypu seem to be suggesting that the couch will get to the buoy before the fog. If so that's wrong. The fog and the couch will get to the buoy at the same time.
Hi Anonymous. That's why I said "read the question" - the fog's, the couch's and the buoy's speeds are all with respect to the river - none are with respect to the land. If none of them were powered, they'd all drift along together.
Now, if the fog and the couch move away from the buoy for an hour, it'll take them an hour to get back as well. Hence a tie.
... an easier way to see it is to pretend that the river isn't flowing.
no the buoy is moving aswell it clearly says that the buoy was pulled along with the current
This post has been removed by the author.
This post has been removed by the author.
I've deleted my last two posts as this one is far better.
To tackle the problem, it is expedient to choose a definite frame of reference. Cam chose to look at the problem from the land, so the speed of the boats have the river speed added or subtracted depending on which way they were moving.
I imagined it from the point of view of the river and/or the buoy, because the river is stationary in that frame and it is easy to see that if a boat sails off at an arbitrary, but constant, speed for an hour, it will also take one hour to return (at the same speed).
So for any boat, at any speed, in any direction, it takes two hours to do the round trip. So, if two boats set of together, they'll arrive back together. It's a tie.
Of course, at the end of those two hours, the buoy and the boats will have travelled an extra 2r nautical miles downstream, where r is the river's speed in knots.
My last paragraph meant with respect to the land.
In the river frame, after 2 hours, the boats are back where they started - by the buoy. The buoy hasn't moved.
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