Reminder
Please note that you are asked to find the velocity of A as observed by B. This is NOT the same thing as vA/B = vA - vB. Do you know why?
However, if you had been asked to find the velocity of B as observed by A, this would be vB/A = vB - vA Do you see why this is true? (Think about the type of motion of the observer in this case vs. the motion of the observer above.)
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Hi, I do not really understand. I managed to find the i component of the v_rel, but apparently to find the j component, I need to find w_ab and I am not sure which method should I use, since the rigid body equations are no longer relevant. What should I do? Thanks for the help.
Recall that the angular velocity that you use in the moving reference frame velocity equation is the "angular velocity of the observer". Since you are asked to use that equation to find the "velocity of A as seen by an observer attached to B", your observer is on aircraft B. Therefore you need to find the angular velocity of aircraft B.
Aircraft B is traveling in a circular path of radius R miles with a speed of v_B. Its heading is changing at the same rate as it turns. Therefore, the motion of B is as if it were attached to a rigid body that is pinned at C. Therefore, you can write the following rigid body VECTOR equation:
v_B = v_C + omega x rB/C = 0 + (omega*k) x (-R*i) = - R*omega*j.
Therefore, as a vector, omega = (- v_B/R)*k .
Does this make sense?
so the omega we need to find is actually for the observer B? Not the omega of A with the center B?
The omega that you use is always the angular velocity of the observer. Once you choose your observer, that sets the omega.
In this case, the problem statement tells you who the observer is.
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