# Find magnitude of two velocities, with one at an angle?

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1. Sep 17, 2016

### Brianna I

• Member advised to use the homework template for posts in the homework sections of PF.
Here is the problem:

I am sure I can use pythagorean theorem of quadratic equation to solve but to be honest I'm blanking ridiculously.
I have tried setting it on a coordinate grid and finding the resultant, but I have had no luck! I know I've done this problem before in highschool but I'm blanking and have spent a few hours now contemplating this.
Thank you!

2. Sep 17, 2016

### Kpgabriel

You could start by breaking up the wind into its x and y components. Remember your trig.

3. Sep 17, 2016

### Brianna I

Hi! I have tried what you said but still do not have the right answer. Here is my work:

Excuse the writing, I'm in a car haha!

4. Sep 17, 2016

### Kpgabriel

Ok, so you found your components for the wind. Now find the components for the glider. look on your graph what angle is the glider traveling?

5. Sep 17, 2016

### Kpgabriel

Sorry, it looks like you already have the components for the resultant vector. So you should have no problem finding the magnitude by using Pythagorean theorem.

6. Sep 17, 2016

### Brianna I

Hi, as you can see I tried that. It did not work :( Do I sum both the x-coordinates? I had 31cos45 - 87 since they are on opposite sides of the coordinate grid.

7. Sep 17, 2016

### Brianna I

Ah, would it be at 180o?

8. Sep 17, 2016

### Kpgabriel

Right, what did that give you?

9. Sep 17, 2016

### Kpgabriel

Yes it would.

10. Sep 17, 2016

### Brianna I

92.037. I checked, not the right answer (for part a)

11. Sep 17, 2016

### Kpgabriel

I am getting a different answer. You have r^2 = (-65.08)^2 + (21.92)^2 ?

12. Sep 17, 2016

### Brianna I

Ah, my mistake. I redid it and got 68.67. I just checked and it is correct! Thank you! I will be able to solve for the angle :)
I must have been too sloppy with the numbers, I realized my calculator was still keeping the negative number even while being squared, messing everything up.
Thanks again!

13. Sep 17, 2016

### Kpgabriel

You're welcome!

14. Sep 18, 2016

### David Lewis

The problem also asks for the direction of the glider's ground track. (In your sketch, the directional sense of vector R is wrong.) It may help to draw the vectors to scale and connect them head to tail to get a preliminary ballpark resultant.