Discover the Boat's Speed: Solving for dc/dt on a Pier with 6m of Rope Out

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In summary, a man on a pier is pulling in a rope attached to a small boat at a rate of 0.4 meters per second. When there is 6 meters of rope out, the boat is approaching the pier at a rate of -0.4 meters per second. The man's hands are 3 meters above the place where the rope is attached and the hypotenuse of the triangle represents the length of the rope. DC/DT is equal to -0.4, as the rope is being pulled in, not let out.
  • #1
asz304
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A man on a pier pulls in a rope attached to a small boat at the rate of 0.4 metres
per second. If his hands are 3 metres above the place where the rope is attached,
how fast is the boat approaching the pier when there is 6 metres of rope out?


Is the question asking for dc/dt ? c is the hypotenuse.
 
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  • #2
Think again about how you are setting up the triangle. Look at it from a 'side-on' view i.e. you are seeing the side of the man's face, as opposed to viewing it from the front.

Which piece represents the hypotenuse? Is it the height of the man's hand from the water, the rope, or the water? What do the other two sides of the triangle represent?
 
  • #3
Yeah? Well the height "y" is fixed is equivalent to 3, and dx/dt is unknown, dc/dt= 0.4, right?
 
  • #4
No, dc/dt = -0.4. The rope is being pulled in (getting shorter), not being let out.
 

Related to Discover the Boat's Speed: Solving for dc/dt on a Pier with 6m of Rope Out

1. How do you determine the boat's speed using this method?

This method involves measuring the change in the length of the rope over time, and using this information to calculate the boat's speed. By measuring the length of the rope at two different points in time, and knowing the distance the boat traveled between those two points, you can solve for the boat's speed using the formula dc/dt = v, where dc is the change in rope length and dt is the change in time.

2. What equipment is needed to perform this experiment?

To perform this experiment, you will need a boat, a pier or dock to tie the rope to, a measuring tape or ruler, a stopwatch or timer, and a calculator to solve for the boat's speed using the formula dc/dt = v.

3. How accurate is this method for determining the boat's speed?

This method can provide a fairly accurate estimate of the boat's speed, but there are some factors that can affect the accuracy of the results. These include the tension of the rope, the accuracy of the measurements, and any external factors that may affect the boat's speed such as wind or currents. It is important to take multiple measurements and calculate an average to improve the accuracy of the results.

4. Can this method be used for boats of any size?

Yes, this method can be used for boats of any size as long as they are able to be tied to a pier or dock and have a rope of at least 6m in length. However, the accuracy of the results may vary depending on the size and weight of the boat.

5. Are there any limitations to using this method?

One limitation of this method is that it only provides the boat's speed in a straight line. If the boat is traveling in a curved path, this method may not accurately reflect its true speed. Additionally, external factors such as wind and currents can affect the accuracy of the results. It is important to take these limitations into consideration when using this method to determine the boat's speed.

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