Using the SUVAT equation for vertical motion: \(s = ut - \frac{1}{2}gt^2\), where \(g = 10 \text{ m s}^{-2}\).

At \(t = 3\) seconds, \(s = 3u - 5 \times 9\).

At \(t = 4\) seconds, \(s = 4u - 5 \times 16\).

Equating the two expressions for \(s\):

\(3u - 45 = 4u - 80\)

Solving for \(u\):

\(3u - 4u = -80 + 45\)

\(-u = -35\)

\(u = 35\)

Substitute \(u = 35\) back into one of the equations for \(s\):

\(s = 3(35) - 45 = 105 - 45 = 60\)

Thus, \(u = 35\) and \(s = 60\).