A sailboat is being propelled westerly by a wind at a speed of 4m/s. If the current is flowing at 2m/s to the?

Question

A sailboat is being propelled westerly by a wind at a speed of 4m/s. If the current is flowing at 2m/s to the northeast, where will the boat be in 10 minutes with respect to its starting postion?
This is for my biomechanics class and I have no idea how to do it. Any help would be nice. Thank You

Answer 1

You need to make a triangle by first drawing an arrow straight left (west), then from the end of that arrow draw a second arrow halfway between straight up and straight right (NE) that's half as long as your first arrow. Then draw the third side of the triangle from where your first arrow started to where your second one ended. That's where the boat will go. The triangle has a 45 degree angle at the left and so you calculate the length of the actual trip (resultant) using Law of Cosines. Then use that length to find the actual angle sailed using either Law of Cosines again or Law of Sines.

Answer 2

This is a classic vector problem.

It can be solved by many methods.

Any way I will provide general solution by graphic method.

Ship has 2 vector acting on it.

1. Vector has direction going or heading west this comes from wind factor. It also has value of 4m/s.

2. Vector has direction going or heading to Northwest this comes from wind factor. It also has value of 2m/s.

Using the parallelogram of forces method and large piece of paper.

Pick a scale of 1in = 1m/s.


Put a point on this paper, call it 'O' for origin, draw a line, if it is a ruled paper, first vector will be 4 in long line, it will run from the point and go left of the point.

Northeast line will be 2 in long and and this will run in that direction from the same point 'O'.

Using the instruments of geometry, complete the parallelogram.

Draw a line from point 'O' to the diagonally opposite point, call it a final point 'F'.

Put the arrow head at 'F' pointing away from 'O'

If you measure this diagonal, it gives you the distance in 1 sec, the direction on the line is the direction in which the boat is moving.

But you are ask to find the distance in ten minute it is suppose be at so multiply by 10.

If the distance was "Y" inches then in 10 minute it is 60x10Y=600Y miles or is it meter. Must be a speed boat,4m/s is 4 miles in 1 second that is fast for a sale boat.

Ha, Ha. It has to be 4 meters per second and 2 metes per secon. Note only units will change Diagram will not change.

So correct answer 600Y meters per second.

Note:
It can be done with Triangle of forces but you will have to be care full about the direction.

Alway use parellelogram of vector method gives correct direction, without fail. Once you get more practise you can use any method.

Answer 3

I remember doing this type of question last year in my Physics class. Unfortanately, I forgot how to set up the equations. All I remember is that you have to separate the northeast current into its north component (which will show you how far north the boat will move) and its east component (which will be going against the wind that the sailboat is being propelled by). Hope this helps!

Answer 4

i imagine the answer is 1800m it is because the relative speed through both the forces comes out to be 3m/s finished time is 600s dis.=speed *time hence finished dis.=1800m eastwards