How Does a Boat's Position Change with Wind and Currents?

[nakidhoboe]

Thanks for the help, sorry I am not really good with Physics and i could use some help please.
Homework Statement
A sailboat is being propelled westerly by the wind at a speed of 4m/s. If the current is flowing at 2m/s to the northeast, where will the boat be in 10minutes with respect to its starting position?

 

[Nex Vortex]

The hardest part of this problem is determining the total velocity. Since the boat is traveling in a single direction, no extra work is needed. However to add the current velocity you must first break it into components (which can be done using the Pythagorean Theorem). Once you find the total velocity, you can use it to find the displacement.

From the information you gave, I'm having a hard time determining exactly what you are having difficulty with. If this doesn't help you get the answer, post back with as much of the problem as you can complete, and I can help you further.

 

[nakidhoboe]

Break into components? by doing 4^4 + 2^2= 20 then 20^1/2 = 4.47?

 

[Nex Vortex]

Alright, I see where you are having troubles now.

Vectors are not like standard numbers that you have been dealing with up until now. They have both a value, and a direction. Therefore, in order to add them, you have to take both into consideration.

First, you need to set up a coordinate system. For this problem it is simple. We can simply call east-west the x-direction and we can call north-south the y-direction.

Now comes the difference between vectors and non-vectors. Different directions cannot simply be added together. You have to do a procedure to separate the directions, which is called breaking the vector into its components.

The first number is 4 m/s west. Since our east-west is on the x-axis, this vector only has one component: -4 m/s on the x-axis (the x-direction is also called the i direction, therefore it can also be written as -4i).

However, the second number is partially in the x-axis and partially on the y-direction. Therefore for this one, we must break it into components in order to add it. Northwest means the vector is at a 45 degree angle between the x-direction and y-direction. If you draw this vector out, it will be much easier to see. In order to find the x and y directions, you will have to use trig functions with the angle and the 2 m/s hypotenuse. You should get (1.41i + 1.41j) for the components. (With j being the y-direction)

When you add these numbers, remember that only the same direction can be added together.

Try to come up with these numbers, and if you need additional help, please don't hesitate to post.

 

[rwisz]

No problem, I am happy to help you with your physics homework. To solve this problem, we can use the concept of vector addition. The boat's velocity due to the wind is 4m/s in the westerly direction. The current's velocity is 2m/s in the northeast direction, which can be broken down into a northward component of 2/sqrt(2) m/s and an eastward component of 2/sqrt(2) m/s.

To find the boat's overall velocity, we can add these two vectors together using the Pythagorean theorem. This gives us a resulting velocity of 4.47m/s in a direction of 45 degrees west of north.

To determine the boat's position after 10 minutes, we need to use the equation d = vt, where d is the distance traveled, v is the velocity, and t is the time. In this case, the boat will have traveled a distance of (4.47m/s)(10 minutes) = 44.7 meters in the direction of 45 degrees west of north.

Therefore, after 10 minutes, the boat will be 44.7 meters in the direction of 45 degrees west of north from its starting position. I hope this helps you understand the problem better and feel more confident in solving physics problems. Keep up the good work!