How do you solve a two dimensional physics probelm

I have two problems for my physics class that I just can't figure out. If anyone can explain step by step how to solve these please help me.

A seagull flies at a speed of 10m/s directly into the wind. Knowing that it takes the bird 25 minutes to travel 8km relative to the earth, find the velocity of the wind. How long will it take the seagull to travel a distance of 12km with the wind?

A butterfly is flying in a gard. First it travels due south for 5m and then 30' degrees west of north for 15 m. Assuming that the positive x direction is east and the positive y direction is north, a) what are the coordinates of the butterfly's final position relative to its initial position and b) what are the magnitude and direction of the displacement of the butterfly (relative to its initial position)?

Thanks!

In the first question the wording is a bit ambiguous.

If it takes 25 minutes to fly 8Km then in must take 25 * 12/8 = 37.5 minutes to fly 12 Km in the same conditions.

Now 8 Km is 8000 m and it takes 25 * 60 sec
So his velocity relative to the earth is 8000/(25 * 60) = 5.33 m/s

As his speed into the wind is 10 then the wind speed relative to the earth must be (5.33 - 10)
= -4.67 m/s (i.e. in the opposite direction.)


Your second question is on vectors and not related to the first.

Vector A is 5 south
Vector B can be resolved into two components 15 * cos (30) North
= 13.0 North
and 15 * sin (30) west
= 7.5 west

Adding the components you then get 13-5 = 8 north
And 7.5 west

Use pythagoras theory to calculate the magnitude.

And atan ( 7.5 / 8) to get the angle ( west of north)

Wrong, Andrew! The seagull is flying WITH the wind, so progress over the ground is (wind speed + his speed in the air), = 15.333m/sec. So it's (12,000/15.333) /60) = 13.044 mins. to cover 12km.

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