Vectors Help: Solving Two Problems

[NIZBIT]

I am stuck on two problems and I keep getting them wrong. Its been a while since I did vectors so I'm a little rusty.

1. Bob walks 200 m south, then jogs 730 m southwest, then walks 200 m in a direction 27.0 degrees east of north. What is the distance and angle?

2. A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0m/s relative to the air, what direction should they head in order to move directly south?

I know these are probably simple, but I'm banging my head on these two. For problem 1, I tried graphically to resolve the vectors using tip to tail but my apporach. Promlem 2 if the wind is blowing from the west so its 6m/s east?

 

[radou]

I am stuck on two problems and I keep getting them wrong. Its been a while since I did vectors so I'm a little rusty.

1. Bob walks 200 m south, then jogs 730 m southwest, then walks 200 m in a direction 27.0 degrees east of north. What is the distance and angle?

Yes, draw the vectors and everything should be prefectly clear.

2. A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0m/s relative to the air, what direction should they head in order to move directly south?

$$\vec{v}_{ducks, total}=\vec{v}_{wind}+\vec{v}_{ducks,relative to wind}$$. The wind vector is known, as is the direction of the final velocity vector of the ducks. Just use the vector equation and the known magnitudes. Solve graphically.

 

[NIZBIT]

I'm getting a rounding or sig fig error on #1. For the distance I got 710.7 so 711?

 

[radou]

I am stuck on two problems and I keep getting them wrong. Its been a while since I did vectors so I'm a little rusty.

1. Bob walks 200 m south, then jogs 730 m southwest, then walks 200 m in a direction 27.0 degrees east of north. What is the distance and angle?

I didn't notice this earlier, but you did not specify in what direction he walks 'east of north'. You can go 'up' or 'down' from there, and depending on that, you get two solutions; one around 800 m, and the other around 1000 m.