A particle moves in the $x - y$ plane under the influence of a force such that its linear momentum is $\overrightarrow{p}(t) = A\lbrack\widehat{i}\cos(kt) - \widehat{j}\sin{(kt)\rbrack}$ Where $A\ $and $k$ are constants. The angle between the force and momentum is

Question

Dr. Abubacker · Accepted Answer

(d) $\overrightarrow{p}(t) = A(\widehat{i}\cos{kt} - \widehat{j}\sin{kt})$
$\overrightarrow{F} = \frac{d}{dt}\left( \overrightarrow{p}(t) ight) = Ak( - \widehat{i}\sin{kt} - \widehat{j}\cos{kt})$
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$\overrightarrow{F}.\overrightarrow{p} = A^{2}k( - \cos{kt}\sin{kt + \sin{kt\cos{kt) = 0}}}$
$	herefore$ The momentum and force are perpendicular to each other at $90{^\circ}$

Q. A particle moves in the $x - y$ plane under the influence of a force such that its linear momentum is $\overrightarrow{p}(t) = A\lbrack\widehat{i}\cos(kt) - \widehat{j}\sin{(kt)\rbrack}$ Where $A\ $and $k$ are constants. The angle between the force and momentum is

Explanation

Reviewed by Dr. Abubacker

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