Motorcyclist gully fall

An undisciplined motorcyclist drove at an unreasonable speed on a mountain road, lost control in a bend, and left the roadway at 90 km/h. He was falling into a gully 36 m deep. Draw a cross-sectional picture of the whole situation.
How far did the motorcycle go, and at what speed?

Final Answer:

x =  67.7285 m
v₂ =  36.4873 m/s

Step-by-step explanation:

$$\begin{gathered} v=90\text{km/h}\to \text{m/s}=90:3.6\text{m/s}=25\text{m/s} \\ y=36\text{m} \\ g=9.81{\text{m/s}}^2 \\ y=\frac{1}{2}\cdot g\cdot t^2 \\ t=\sqrt{2\cdot y/g}=\sqrt{2\cdot 36/9.81}\doteq 2.7091\text{s} \\ x=v\cdot t=25\cdot 2.7091\text{m}=67.7285\text{m} \end{gathered}$$

$$\begin{gathered} v_1=g\cdot t=9.81\cdot 2.7091\doteq 26.5767\text{m/s} \\ {v}_2=\sqrt{v^2+v_1^2}=\sqrt{25^2+26.5767^2}=36.4873\text{m/s} \end{gathered}$$

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