The problem starts by saying that an aircraft is flying such that it's longitudnal axis always points towards the point (0,0). The plane itself starts at some point on the x axis (say like (10,0)). The plane always has a constant airspeed, and experiences a constant wind blowing "north"(adsbygoogle = window.adsbygoogle || []).push({});

We want to find the path the aircraft takes

My solution so far:

Let s1=speed of the plane

s2=speed of the wind

theta=angle of the plane at time t

Find sin(theta) and cos(theta) in terms of x and y:

y=r sin(theta) and x=r cos(theta)

I think this is right if I remember my calc correctly, but I am not sure if r can be written using the speeds s1 and s2?

The next part of the question asks us to find dx/dt and dy/dt in terms of x,y,s1, and s2:

I am not sure how to do this part. I think I should break up the planes velocity into its components parallel to the axis but that is as far as I have gotten. If I could have help here I think I could finish the rest of the problem, but I don't want to mess up my initial work and do the whole problem wrong.

Thanks

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# Differential equation word problem

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