A 4.0-m-diameter playground merry-go-round, with a moment of inertia of \(400 \mathrm{~kg} \cdot \mathrm{m}^{2}\), is freely rotating with an angular velocity of \(2.0 \mathrm{rad} / \mathrm{s}\). Ryan, whose mass is \(80 \mathrm{~kg}\), runs on the ground around the outer edge of the merry-go-round in the opposite direction to its rotation. Still moving, he jumps directly onto the rim of the merry-go-round, bringing it (and himself) to a halt. How fast was Ryan running when he jumped on?

A. \(2.0 \mathrm{~m} / \mathrm{s}\)

B. \(4.0 \mathrm{~m} / \mathrm{s}\)

C. \(5.0 \mathrm{~m} / \mathrm{s}\)

D. \(7.5 \mathrm{~m} / \mathrm{s}\)

E. \(10 \mathrm{~m} / \mathrm{s}\)