A rod length AB is moving with ends remaining in contact with frictionless wall and floor. If at the instant shown, the velocity of the end B is 3 m s - 1 towards the negative x -direction, then the m

Question

A rod length AB is moving with ends remaining in contact with frictionless wall and floor. If at the instant shown, the velocity of the end B is 3 m s - 1 towards the negative x -direction, then the magnitude of the velocity of the end A will be

TestHub · Accepted Answer

From geometry, it is clear that x = l cos ⁡ θ and y = l sin ⁡ θ ∴ v x = d x d v = - l sin ⁡ θ d θ d t and v y = d y d t = l cos ⁡ θ d θ d t ∴ v y v x = - cot ⁡ θ or v y = - v x cot ⁡ θ Since, v x = - 3 m s - 1 , hence v y = - - 3 cot ⁡ 60 ° = 3 × 1 3 = 3 m s - 1

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