We are learning about relative motion 2D in my physics class and were given the

Question

We are learning about relative motion 2D in my physics class and were given the question:

A bird wishes to fly due north with a speed of 10 m/s relative to the ground. There is a wind directed from southwest to northeast with a speed of 5 m/s. How fast must the bird fly relative to the wind and at what angle must the bird aim at the wind?

Im not sure if i did it right. I used the vector eqation: Vbw = Vb - Vw. Then broke it up into compenents: Vbwx = Vbx - Vwx and Vbwy = Vby - Vwy. For my Vbwx and Vbwy I got 3.5m/s for each one. I found it by assuming that the wind made a 45-45-90 triangle, and used to it to find the Vwx and Vwy. Not sure if I am suppose to do it like that. After that I plugged those into my components equations and then used a^2+b^2 = c^2 to find the velocity of Vbw and got 7.4 m/s. Then i found the angle to be 28 degrees. Again im not sure if I did this problem right.

Explanation / Answer

Yest, You have done it correctly :). For explanation ->

We have to break the wind's velocity into two components

which will both be 5/root(2) = 3.535 m/s

Now bird should move 10m/s with respect to ground in north direction.

Hence bird should not move at all in east-west direction with respect to ground, hence it should move with 3.535m/s in west direction with respect to wind.

Similarly in north direction, velocity with respect to ground is 10m/s; since wind is already moving at 3.535, so bird needs extra 10-3.535 to make it. hence 6.465 m/s

For net velocity we can square these two and add and take root, which gives us, ~7.4 m/s. This should be in north-west direction

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