Horizontal motion:
\( \Delta x = v_0 \cos \theta \times t \)

Vertical motion:
\( \Delta y = v_0 \sin \theta \times t – \dfrac{1}{2} g t^2 \)

Since \( t = \dfrac{\Delta x}{v_0 \cos \theta} \), substitute into vertical equation:
\( -2.0 = v_0 \sin 30^\circ \times \dfrac{54}{v_0 \cos 30^\circ} – \dfrac{1}{2} \times 9.8 \times \left( \dfrac{54}{v_0 \cos 30^\circ} \right)^2 \)

\( -2.0 = 54 \tan 30^\circ – \dfrac{1}{2} \times 9.8 \times \dfrac{54^2}{v_0^2 \cos^2 30^\circ} \)

Calculate constants:
\( \tan 30^\circ = \dfrac{\sqrt{3}}{3} \approx 0.5774 \)
\( \cos 30^\circ = \dfrac{\sqrt{3}}{2} \approx 0.8660 \)

Substitute values and solve for \( v_0 \):

\( -2.0 = 54 \times 0.5774 – \dfrac{4.9 \times 54^2}{v_0^2 \times 0.75} \)
\( -2.0 = 31.176 – \dfrac{14,289.6}{0.75 v_0^2} \)
Rearranging:
\( 31.176 + 2.0 = \dfrac{14,289.6}{0.75 v_0^2} \)
\( 33.176 = \dfrac{14,289.6}{0.75 v_0^2} \)
\( v_0^2 = \dfrac{14,289.6}{0.75 \times 33.176} \)
\( v_0^2 \approx 574.6 \)
\( v_0 \approx 23.98 \) m/s

Use \( v_f^2 = v_i^2 + 2 a s \)
\( v_i = 0 \) (starts from rest), \( v_f = v_0 \), \( s = 0.70 \) m
\( (23.98)^2 = 0 + 2 a \times 0.70 \)
\( a = \dfrac{(23.98)^2}{2 \times 0.70} \)
\( a \approx 410.4 \) m/s²

\( t = \dfrac{\Delta x}{v_0 \cos \theta} \)
\( t = \dfrac{54}{23.98 \times 0.8660} \)
\( t \approx 2.60 \) s