Question

A particle moves in the x-y plane under the influence of a force such that the linear momentum is p(t) = a [ cos kt - sin kt ] where a and k are constants. The angle in degrees between force and momentum is

Answer 1

Answer:

90 degree

Explanation:

We know that, p(t)= a ( icoskt - jsinkt )

As F= dP/dt

       = d[a (icoskt - jsinkt )] / dt

       = ak (- isinkt - jcoskt)

Then dot product of F and P is: (where A is angle between F and P)

cos A= (F.P) / |F|.|P|

        = {[ak (- isinkt - jcoskt )] . [a (icoskt - jsinkt )]} / (a*ak)

        = {(a^2k) (-sinkt coskt + sinkt coskt)} / (a^2k)

        = 0

        = cos 90

Therefore angle between F and P is 90 degree

Answer 2

hlo mate here is ur ans.....................................

Answer

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1

enoosap9

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Answer:

90 degree

Explanation:

We know that, p(t)= a ( icoskt - jsinkt )

As F= dP/dt

      = d[a (icoskt - jsinkt )] / dt

      = ak (- isinkt - jcoskt)

Then dot product of F and P is: (where A is angle between F and P)

cos A= (F.P) / |F|.|P|

       = {[ak (- isinkt - jcoskt )] . [a (icoskt - jsinkt )]} / (a*ak)

       = {(a^2k) (-sinkt coskt + sinkt coskt)} / (a^2k)

       = 0

       = cos 90

Therefore angle between F and P is 90 degree...................