Initial speed: \( u_0 = 0 \, \text{m/s} \)
Acceleration: \( a_1 = 3.5 \, \text{m/s}^2 \)
Time: \( t_1 = 10 \, \text{s} \)

\( v_1 = u_0 + a_1 t_1 \)
\( v_1 = 0 + (3.5)(10) = 35 \, \text{m/s} \)

\( s_1 = u_0 t_1 + \tfrac{1}{2} a_1 t_1^2 \)
\( s_1 = 0 + \tfrac{1}{2} (3.5)(10)^2 = 175 \, \text{m} \)

Reaction time: \( t_r = 0.6 \, \text{s} \)
\( s_{\text{react}} = v_1 t_r \)
\( s_{\text{react}} = (35)(0.6) = 21 \, \text{m} \)

Distance ahead when noticing ramp: \( 50 \, \text{m} \)
Remaining distance after reaction: \( d_{\text{remain}} = 50 – 21 = 29 \, \text{m} \)

Braking acceleration: \( a_2 = -7.2 \, \text{m/s}^2 \)
\( v^2 = u^2 + 2 a s \)
\( 0 = (35)^2 + 2(-7.2) s_{\text{brake}} \)
\( s_{\text{brake}} = \dfrac{(35)^2}{2 \times 7.2} \approx 85.07 \, \text{m} \)

\( v^2 = u^2 + 2 a s \)
\( v^2 = (35)^2 + 2(-7.2)(29) \)
\( v^2 = 1225 – 417.6 = 807.4 \)
\( v = \sqrt{807.4} \approx 28.43 \, \text{m/s} \)

Ramp angle: \( \theta = 27^\circ \)
\( v_x = v \cos \theta = (28.43) \cos 27^\circ \approx 25.34 \, \text{m/s} \)
\( v_y = v \sin \theta = (28.43) \sin 27^\circ \approx 12.91 \, \text{m/s} \)

Vertical motion equation:
\( y = v_y t – \tfrac{1}{2} g t^2 \)
Height difference: \( y = -3 \, \text{m} \)
\( -3 = (12.91) t – 4.9 t^2 \)
Rearranged to quadratic: \( 4.9 t^2 – 12.91 t – 3 = 0 \)
Solved for \( t \):
\( t = \dfrac{12.91 \pm \sqrt{12.91^2 – 4 \times 4.9 \times (-3)}}{2 \times 4.9} \)
\( t \approx 2.85 \, \text{s} \)

\( \Delta x = v_x t \)
\( \Delta x = (25.34)(2.85) \approx 72.22 \, \text{m} \)

\( v_{y_{\text{final}}} = v_y – g t \)
\( v_{y_{\text{final}}} = 12.91 – (9.8)(2.85) \approx -15.02 \, \text{m/s} \)

\( v_{\text{final}} = \sqrt{v_x^2 + v_{y_{\text{final}}}^2} \)
\( v_{\text{final}} = \sqrt{(25.34)^2 + (-15.02)^2} \approx 29.46 \, \text{m/s} \)

Direction angle:
\( \theta_{\text{final}} = \arctan\left( \dfrac{|v_{y_{\text{final}}}|}{v_x} \right) \)
\( \theta_{\text{final}} = \arctan\left( \dfrac{15.02}{25.34} \right) \approx 30.7^\circ \) below horizontal