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Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the left is 10 m/s. What is the velocity of B when angle α = 60°?

1. 5.8 m/s
2. 9.8 m/s
3. 10 m/s
4. 17.3 m/s

Correct answer: 17.3 m/s

Solution

The velocity of B can be determined using the constraint relation for the rigid rod. The velocity components of A and B must satisfy the condition that the length of the rod remains constant. Using trigonometry, the velocity of B is given by v_B = v_A / sin(α). Substituting v_A = 10 m/s and α = 60°, we get v_B = 10 / sin(60°) = 10 / (√3/2) = 20/√3 ≈ 17.3 m/s.

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