Problems involving frames of reference and relative velocity

[Byrgg]

I have a few questions here, and I'm stuck/confused on some of them. Here they are:

1. The air speed of a small plane is 215 km/h.The wind is blowing at 57 km/h from the west. Determine the velocity of the plane relative to the ground if the pilot keeps the plane aimed in the direction [34 degrees E of N].

I'm not really sure about this one, it seems a little different from the examples the teacher showed us in class. I'm not really sure which angle the angle mentioned is referring to, basically, I just need help figuring out how to set up the problem, and then I should be able to continue without problems from there(I hope).

2. Two kayakers can move at the same speed in calm water. One begins kayaking straight across a river, while the other kayaks at an angle upstream in the same river to land straight across from the starting position. Assume the speed of the kayakers is greater than the speed of the river current. Which kayaker reaches the far side first? Explain why.

I don't really know how to figure this out. You have one who is angled so that they partially face upstream, and then one trying to go straight ahead, but the river will alter their direction, so they'll be angled facing downstream. Which gets there first? I don't know, they are both traveling at the same speed(I'm assuming), but in different directions. I'm a little confused about this whole thing, any help here would be appreciated.

3. A pilot is required to fly directly from London, UK, to Rome, Italy in 3.5 h. The displacement is 1.4 x 10^3 hm [43 degrees E of S]. A wind is blowing with a velocity of 75 km/h [E]. Determine the required velocity of the plane relative to the air.

For this one, I got pretty far, and it seems as though I got the magnitude of the velocity right(it matched the answer in the back of the book), but my angle seemed off. If someone could help me figure out the proper way to figure out the angle, then I'd be greatful. If you want me to show the work that I've done, or make a diagram, I'll try to do so(mind you, the diagram may be hard for me to draw accurately, it will just be approximate).

 

[Integral]

Draw pictures, lable all of the quanities, then use what you should know about vector addition. Your drawings do not need to be precise, just good enough to show the relationships. Lable angles and magnetudes, break them down into components and add 'em up.

 

[Byrgg]

That applies for all of these situations, right? I didn't really know how to draw the diagram for the first one, and the second I found hard to work with in general.

 

[Byrgg]

Could some one give me some more help please? I'm still confused about these questions.