Solve the Ship & Rope Problem: Find Time for Rope to be Wet

  • Thread starter Chaulesh
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In summary, a boat with a height of 15 meters has a rope hanging from its deck at a distance of 7.5 meters above sea-level. With the sea-level rising at a constant rate of 1.75 cm/s, the rope will be wet when the sea-level reaches a height of 7.5 meters. This will occur after approximately 428.57 seconds, as long as it starts raining immediately.
  • #1
Chaulesh
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So this one should be simple to solve with some maths.

There is a boat of height 15 metres (measured from sea-level) and there is a rope hanging from its deck so that the distance from the sea-level is half the third of the boat's height.

It is given that the sea-level is rising at the constant rate of 1.75 cm/s. After how much time will the rope be wet?
 
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  • #2
As soon as it starts raining.
 
  • #3
As sea level will rise, ship will also go up. The rope tied to deck will also go up and will not touch sea level.
 

1. How do I calculate the time it takes for the rope to become wet?

In order to solve the ship and rope problem, you must first understand the variables involved. The time it takes for the rope to become wet depends on the speed of the boat, the length of the rope, and the angle at which the rope is hanging. This can be calculated using trigonometry and basic physics principles.

2. Can you provide an example of how to solve the ship and rope problem?

Yes, let's say the boat is traveling at a speed of 10 knots (nautical miles per hour) and the rope is 50 feet long. The angle at which the rope is hanging is 45 degrees. Using the formula t = l / v * cos(theta), we can calculate the time it takes for the rope to become wet as 50 feet / (10 knots * cos(45 degrees)) = 7.07 seconds.

3. What factors can affect the time it takes for the rope to become wet?

Aside from the boat's speed, rope length, and angle, there are other factors that can affect the time it takes for the rope to become wet. These include wind speed, water current, and the type of material the rope is made of. These variables may make the calculation more complex, but the same principles and formulas can still be used.

4. Is the ship and rope problem applicable in real life situations?

Yes, the ship and rope problem has real-life applications in fields such as marine navigation, engineering, and physics. It can also be used as a practical example in teaching trigonometry and other mathematical concepts.

5. Can the ship and rope problem be solved using other methods besides trigonometry?

Yes, there are other methods that can be used to solve the ship and rope problem, such as using kinematics equations or using a graphical approach. However, trigonometry is often the most straightforward and efficient method for solving this type of problem.

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