Given:

• Mass \(m = 1.6 \text{ kg}\)
• Initial speed \(u = 20 \text{ m/s}\)
• \(\tan \alpha = \frac{3}{4} \Rightarrow \sin \alpha = \frac{3}{5}\)

Using the conservation of energy, the initial kinetic energy is converted into gravitational potential energy:

\(\frac{1}{2} m u^2 = m g x \sin \alpha\)

Substitute the known values:

\(\frac{1}{2} \times 1.6 \times 20^2 = 1.6 \times 9.8 \times x \times \frac{3}{5}\)

\(320 = 9.6x\)

Solve for \(x\):

\(x = \frac{320}{9.6} = 33.3 \text{ m}\)