For particle Q, using the equation of motion for free fall:

\(3.2 = \frac{1}{2} g t^2\)

Solving for t, we get:

\(t = \sqrt{\frac{2 \times 3.2}{g}} = 0.8 ext{ s}\)

For particle P, using the equation of motion along the ramp:

\(s = ut + \frac{1}{2} a t^2\)

Where a is the component of gravitational acceleration along the ramp:

\(a = g \sin 30° = 0.5g\)

Substituting the values:

\(6.4 = u(0.8) + \frac{1}{2} (0.5g)(0.8)^2\)

Solving for u:

\(u = 6 ext{ m s}^{-1}\)

To find the speed of P at the bottom, use:

\(v^2 = u^2 + 2as\)

Substitute the known values:

\(v^2 = 6^2 + 2 \times 0.5g \times 6.4\)

Solving for v:

\(v = 10 ext{ m s}^{-1}\)