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