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A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through an angle θ(t) about the hinge. At time t, L(t) = 1 m, L̇(t) = 1 m/s, θ(t) = π/4 rad and θ̇(t) = 1 rad/s. The magnitude of the velocity of the other end of the rod is

1. 1 m/s
2. √2 m/s
3. √3 m/s
4. 2 m/s

Correct answer: √2 m/s

Solution

The end velocity has radial component Ldot = 1 m/s and transverse component L*thetadot = 1*1 = 1 m/s. Magnitude = sqrt(1^2 + 1^2) = sqrt(2) m/s (index 1).

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