Don't Miss the Boat: Get Onboard in 10cm or Less

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In summary, the boat will only board if it is within 10 cm of the dock at the highest point in its up-and-down motion. You can calculate the time until the boat is within 10 cm of the dock by using arccos(0.1/0.2).
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iwonde
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Homework Statement


While on a visit to Minnesota, you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple harmonic motion with amplitude 20cm. The boat takes 3.5 s to make one complete up-and-down cycle. When the boat is at its highest point, its deck is at the same height as the stationary dock. As you watch the boat bob up and down, you (mass 60 kg) begin to feel a bit woozy, due in part to the previous night's dinner. As a result, you refuse to board the boat unless the level of the boat's deck is within 10 cm of the dock level. How much time do you have to board the boat comfortably during each cycle of up-and-down motion?


Homework Equations





The Attempt at a Solution


I don't really understand the problem. So am I finding the time intervals in which the level of the deck is within 10cm of the dock level? How should I approach this problem?
 
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  • #2
A graph of simple harmonic motion looks like what function?
 
  • #3
The motion has amplitude 20cm, you will only board if the boat is within 10cm of the dock, i.e. within 10 cm of its highest point in its motion. Draw a graph of the motion the boat executes and the answer should be easier to get.
 
  • #4
qspeechc said:
The motion has amplitude 20cm, you will only board if the boat is within 10cm of the dock, i.e. within 10 cm of its highest point in its motion. Draw a graph of the motion the boat executes and the answer should be easier to get.

I'm bringing back a really old question but it just happens that I have the same HW question...

I understand that the graph of simple harmonic motion is sin/cos, and the highest point corresponds to the 20 cm and then half of that will be 10 cm. But how do i figure out the time from that alone?
 
  • #5
Sorry to bump this thread, but how do I solve this problem? The amplitude is given as 0.2 m. The boat can only be boarded when it's within 0.1 m of the dock, so x = 0. T=2*Pi*sqrt(m/k), which means k must equal 4834 N/m, implying that omega is 1.795.

x = A*cos(omega*t)
0.1 = 0.2*cos(1.795*t)

How do I solve for t?

edit:

arccos(0.1/0.2)/1.795, but it gives 0.583 seconds. The answer is 1.17 seconds, or arccos(-0.1/0.2)/1.795. Why is it -0.1 (or -0.2, whichever it is)?
 
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1. What is "Don't Miss the Boat: Get Onboard in 10cm or Less" about?

"Don't Miss the Boat: Get Onboard in 10cm or Less" is a scientific concept proposed by a group of researchers. It suggests that in order to combat the effects of sea level rise, humans should start building structures that can withstand water levels rising by 10cm or less.

2. How does this concept relate to climate change and rising sea levels?

This concept is directly related to climate change and rising sea levels because it addresses the potential impacts of these issues. As sea levels continue to rise, coastal cities and communities will face greater risks of flooding and damage. This concept offers a potential solution to mitigate those risks.

3. What kind of structures would be able to withstand water levels rising by 10cm or less?

The specific types of structures that would be able to withstand water levels rising by 10cm or less would depend on various factors such as location, materials used, and design. However, some examples could include elevated buildings, sea walls, and floating structures.

4. Is this concept feasible and cost-effective?

While more research and development would be needed to fully determine the feasibility and cost-effectiveness of this concept, initial studies have shown promising results. The use of innovative technologies and materials could potentially make this concept both feasible and cost-effective in the long run.

5. What are the potential benefits of implementing this concept?

The potential benefits of implementing this concept include minimizing the impacts of sea level rise on coastal communities, protecting valuable infrastructure and property, and potentially reducing the need for costly flood prevention measures in the future.

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