a
The acceleration of a sphere down the inclined plane is given

by,

\(a=\frac{g \sin \theta}{1+\frac{k^{2}}{r^{2}}}\)

The moment of inertia of the sphere is given by,

\(I=\frac{2}{5} m r^{2}\)

\(=m k^{2}\)

Consider above,

\(\frac{k^{2}}{r^{2}}=\frac{2}{5}\)

Use the equation,

\(v^{2}=2 a s\) \(...(I)\)

Substitute \(2.8\) for \(v, \frac{2}{5}\) for \(\frac{k^{2}}{r^{2}}, 30^{\circ}\) for \(\theta\) and \(\frac{g \sin \theta}{1+\frac{k^{2}}{r^{2}}}\) for \(a\) in

equation \((I)\)

\(2.8^{2}=2\left(\frac{g \sin 30^{\circ}}{1+\frac{2}{5}}\right) s\)

\(=2\left(\frac{2(10)\left(\frac{1}{2}\right)}{\frac{7}{2}}\right)\)

\(s=2.8^{2}\left(\frac{7}{20}\right)\)

\(=2.744 m\)