#### danago

Gold Member

- 1,122

- 4

Two boats are moving along straight paths and their position vectors at noon are:

For the first question, i assumed its initial position would be 0 hours after noon. So i just answered it as:[tex]\mathbf{r}_1=(7-4t)\mathbf{i}+(-5+t)\mathbf{j}[/tex]

[tex]\mathbf{r}_1=(12-3t)\mathbf{i}+(13-t)\mathbf{j}[/tex]

a) where was the first boat initially?

b) Where was the second boat relative to the first boat initially?

c) What is the velocity vector, [tex]\mathbf{v}_2[/tex], of the second boat?

d) find weather or not the boats will colide.

[tex]7\mathbf{i}-5\mathbf{j}[/tex]

Now i wouldnt have a clue if thats even close to being correct, but its the only decent answer i could come up with.

For the next part, i drew the diagram, and just found a vector going from the position of the first boat to the second, from the initial positions, which gave me the final vector:

[tex]4\mathbf{i}+18\mathbf{j}[/tex]

For part c, the velocity of the second boat, i just wrote how much the position vector increases for every incriment of t. I came up with:

[tex]-3\mathbf{i}-\mathbf{j}[/tex]

The problem with this was that the question said they were travelling in a straight line, and if i apply this velocity, then they change their direction. So im lost.

And with the final question, im stuck, because i cant really do it until i answer the previous ones correctly.

So if anyone doesn't mind, please put me on the right track for these questions, because i highly boubt ive answered them correctly.

Thanks,

Dan.