# Board the Boat When It's Within 10cm of the Dock

• Ronnin
In summary, the conversation discusses finding the time interval to board a boat on a lake that is exhibiting simple harmonic motion with an amplitude of 20cm and a period of 3.5s. The boat must be within 10cm of the dock for boarding. The participants mention using the equation y(t) = A*sin(omega*t+delta) to find when y(t) is greater than 10cm. They also suggest restricting the domain to one time period for easier calculation.
Ronnin
A boat(1500kg) is on a lake exibiting SHM with an amp of 20cm bobbing on the waves. The boat takes 3.5s to make one complete up and down cycle. When the boat is at its highest point it is at the same level as the dock. You will only board the boat if it is within 10cm of the dock. How much time do you have to board the boat per cycle.

Can someone give me a hint on how to start with this problem. I know I'm looking for the interval in the sine wave where f(x) is greater than 10cm. Any ideas?

Do you know the general expression for representing the vertical displacement of SHM?

it it x(t)=Asin(omega*t+delta)? Am I thinking about the right formula?

Ronnin said:
it it x(t)=Asin(omega*t+delta)? Am I thinking about the right formula?

Yes, you are. It would be more appropriate to call it y(t) in this case, but it doesn't really mater.

Still need a little help. Not quite sure how the math is supposed to work in this one.

Okay so your looking for the time interval of t when y(t)>0.1; so the first thing we need to do is find when y(t)=0.1,

$$A\sin\left(\omega \cdot t)=0.1$$

Now, can you solve for t?

Edit: It may also be useful to restrict our domain here to something like;

$$dom\left[ 0,\frac{1}{f} \right]$$

So that we only consider one time period.

Last edited:
Sorry Hoot, that's the part I don't remember. I'm rusty on the how the trig works here. Can I just take the sin inverse for each side of the equation?

Ronnin said:
Sorry Hoot, that's the part I don't remember. I'm rusty on the how the trig works here. Can I just take the sin inverse for each side of the equation?
Yes, sounds good to me, although I would divide through by A beforehand. Also take note of the edit in my above post.

## What does "Board the Boat When It's Within 10cm of the Dock" mean?

This phrase refers to the recommended distance between the boat and the dock for safe boarding. It is generally considered safe to board when the boat is within 10cm (approximately 4 inches) of the dock.

## Why is it important to board the boat when it's within 10cm of the dock?

Boarding the boat when it is within 10cm of the dock ensures that you have a secure and stable platform for getting on and off the boat. This minimizes the risk of falls or accidents.

## What happens if I try to board the boat when it's not within 10cm of the dock?

Attempting to board the boat when it is not within 10cm of the dock can be dangerous. The boat may be unstable and could shift unexpectedly, causing you to lose your balance and potentially fall into the water or onto the dock.

## Is it safe to board the boat when it's within 10cm of the dock in all weather conditions?

No, it is not always safe to board the boat when it is within 10cm of the dock, especially in rough weather conditions. It is important to assess the conditions and use your best judgment to determine if it is safe to board.

## Are there any alternative methods for boarding the boat besides waiting for it to be within 10cm of the dock?

Yes, there are alternative methods for boarding the boat, such as using a boarding ladder or having someone assist you. However, it is generally recommended to wait for the boat to be within 10cm of the dock for the safest and most stable boarding experience.

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