Friday, February 2, 2018

homework and exercises - Relative motion involving angle


Suppose I am going in a direction with a velocity v1 and my friend is going in a direction which makes an angle of A with my direction with a velocity of v2.


Then what will be my relative motion with respect to my friend or his relative motion with respect to me?



Every book I have read gave example where two things are going parallel or opposite of me. But I've never found any example with an angle.



Answer



Let's say your velocity is v1 is v1=v1xˆi+v1yˆj and your friends velocity v2 is v2=v2xˆi+v2yˆj Then your velocity relative to your friend will be vr=(v1xv2x)ˆi+(v1yv2y)ˆj The components can be found by considering an appropriate coordinate system. In this case that will be a coordinate system with the x-axis aligned with your friends velocity. In that case v2y=0. While the components of your velocity will be v1x=v1cosA and v1y=v1sinA.


Hope this helps.


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