# Jet Skis vector homework

1. Jun 10, 2009

Two people take identical Jet Skis across a river, traveling at the same speed relative to the water. Jet Ski A heads directly across the river and is carried downstream by the current before reaching the opposite shore. Jet Ski B tavels in a direction that is 35 degrees upstream and arrives at the opposite shore directly across from the starting point. a) Which Jet Ski reaches the opposite shore in the least amount of time? b.) Confirm your answer to part a by finding the ratio of the time it takes for the two Jet Skis to cross the river.

2. Jun 10, 2009

### LowlyPion

Re: Vectors

What have you tried?

3. Jun 10, 2009

### belliott4488

Re: Vectors

Interesting problem. Is there anything in particular you wanted to discuss about it?

4. Jun 10, 2009

Re: Vectors

OKay so I figured out that Jet Ski gets there faster and now I have to find the ratio of the time...and I think I do that by doing something like showing how Vsw + Vwg with sw meaning skier on the water and gw meaning the ground water....I was thinking of assigning random numbers for A and B and then showing how from there but the thing is I dont really know how to prove it.....I just know because of common sense that Skier A will reach there faster..... what do you guys think?

5. Jun 10, 2009

Re: Vectors

sorry Jet Ski A ** gets there faster

6. Jun 10, 2009

### tiny-tim

Use a vector triangle for each Jet Ski …

what do you get?

7. Jun 10, 2009

Re: Vectors

A is like x
and B is like y

should I do something like cos(35) to get x and then do something from there?

8. Jun 10, 2009

Re: Vectors

9. Jun 10, 2009

### tiny-tim

vector triangle

Do you know what a vector triangle is?

Have you been shown how to draw one?

10. Jun 10, 2009

Re: Vectors

No, I have no idea what a vector triangle is.

11. Jun 10, 2009

Re: Vectors

12. Jun 10, 2009

Re: Vectors

okay so it is something about all the points of the triangle meeting at the same point which works because the skiers do eventually meet at the same point but one just gets there faster than the other.

13. Jun 10, 2009

### tiny-tim

ok … velocities are vectors, and so they obey the vector law of addition

in other words, you can add velocities the same way you add vectors.

For the second Jet Ski, draw arrows representing the three velocities …

that's VBR, the velocity of B relative to the river,

VBG, the velocity of B relative to the ground,

and VRG, the velocity of the river relative to the ground.

Those three vectors should make a closed-up triangle.

Then do a triangle for A also, and then put the two triangles next to each other

14. Jun 10, 2009

Re: Vectors

so if I drew this correctly the first and second velocities relative to the water is the same....but I don't really know. I don't understand what I am doing. Why would the speed relative to the water be the same...shouldn't they be different because skier number 2 is going at an angle and gets to the shore after skier number 1 ? I am unbelievably confused!

15. Jun 10, 2009

Re: Vectors

and how am I supposed to get the time ratio from all this?

16. Jun 10, 2009

### LowlyPion

Re: Vectors

Draw the vectors out.

In both cases you have a right triangle don't you?

Except in the one case you have traveled the length of the hypotenuse.
In the other you traveled one leg.

What is the ratio of that leg to the hypotenuse? Anything pop to mind?

17. Jun 10, 2009

### LowlyPion

Re: Vectors

Because that's the only speed the jet ski can go. It's going constant velocity in the water. The vector of the current moves it, but in the water frame of reference it is still going the same speed whether up stream or down.