A particle moves with a velocity v = (4 i - 2 j + c k ) ~m~s ⁻¹ under the influence of a constant force F = (5 i + 3 j - 4 k ) ~N . If the instantaneous power supplied to the particle is 2 ~W , the value of the unknown component c is:

Step-by-step solution

Instantaneous power is given by the dot product of force and velocity vectors: P = F v Given F = (5 i + 3 j - 4 k ) ~N and v = (4 i - 2 j + c k ) ~m~s ⁻¹ , we have: P = (5)(4) + (3)(-2) + (-4)(c) P = 20 - 6 - 4c = 14 - 4c We are given that the power P = 2 ~W . Equating the two: 14 - 4c = 2 4c = 12 c = 3 Answer: 3