Boat and Dock
You are sitting in a small boat, holding at the end of a rope. The other end of the rope is tied to the top of the nearby pier, such that it is higher above the water than your end of the rope. You pull on the rope, causing your boat to move toward the pier, stopping directly underneath the pier.
As you pull on the rope, which is faster, the speed the boat moves across the water or the speed the rope moves through your hands ?
As you pull on the rope, which is faster, the speed the boat moves across the water or the speed the rope moves through your hands ?
Labels: mathemagic
posted by Rajesh Lal at
9:41 PM
10 Comments:
FASTER IS THE ROPE
rope..
This is assuming that the pulling of the rope is at a steady pace: For every foot that you pull on the rope, the pier comes a foot closer. Technically the rope would be ahead of you by milliseconds because of physics (reaction time). But only fractionally. So they are virtually the same speed but one is behind the other. (like two cars on the interstate both going 60 mph, one can be ahead of the other but be going the same speed as the other.)
The boat moves faster.
It's a right triangle.
The hypotenuse is shorter than the height and width put together.
So as you pull at first, it will seem about the same, then as you go along, the rope will go slower and slower while your boat could continue at the same speed.
-Deep
...If it was a pulley system (to make it easier), then the answer would be the rope.
-Deep
It's relative
The people who get it right dont bother explaining to the others..so I will.
The rope is faster because the length of rope is longer than the distance between the pier and the boat, but you reach the end of the rope at the same time your boat reaches the pier.
(we know there is more rope than distance in the water because the hypotenuse is always LONGER than either side of the triangle)
For example, if there is 10m to the pier, and 15m of rope, and it takes you 1 minute to get to the pier, the speeds are as follows:
rope--15m/min
boat--10m/min
So the rope is always traveling faster. Period.
So your assumption is that you are actually using all the rope... which unless you are standing up and are actually as tall as the pier is... is completely a load of #@$%
At first the rope and the boat and the rope are almost the same.
However, as the boat approaches the pier, and you go under the pier the boat will defintely be going faster than the rope.
For Anon. #5 you state the rope--15m/min; but you remember that speed =distance x time, but the rope shortens as it goes and you forgot to account for the height of the pier.
Eventually the boat will be moving faster than the rope because the rope will be behind you as you are under the pier
Good going Patrick. It is a trig problem and the boat will become increasingly faster until it reaches directly below the pier. say you are 100 units from where the boat will end up which we say is 4 units below where the rope is tied to the pier. you will need 100.08 units or more of rope but will use 96.08 units to pull the boat 100 units. remember sq root of a^2 + b^2 = c^2
a=100 b=4 c=100.08 your angle of rope will start out at 2.29 degrees and increase to 90 deg. as you come closer to the pier. at any given point you can figure your relationship of your ropelength to distance giving you a ratio of rope speed to boat speed. i like these puzzles of math.
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