A particle moves in x-y plane under the influence of a force F such that its linear momentum is P(t) = î cos(kt) - ĵ sin(kt). If k is constant, the angle between F and P will be :
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A particle moves in x-y plane under the influence of a force F such that its linear momentum is P(t) = î cos(kt) - ĵ sin(kt). If k is constant, the angle between F and P will be :

G1 Physics · Accepted Answer

Given: P = î cos(kt) - ĵ sin(kt) Magnitude of P is constant. Force is the rate of change of momentum: F = dP/dt = -kî sin(kt) - kĵ cos(kt) Now: F · P = [-k sin(kt)][cos(kt)] + [-k cos(kt)][-sin(kt)] = 0 Therefore: cosθ = 0 Hence: θ = π/2