a) As funções de posição serão:

\(\begin{align} & S=\frac{v\sin 2\theta }{g} \\ & 54,52=\frac{v\sin 2\theta }{9,8} \\ & v=\frac{531}{\sin 2\theta } \\ & \\ & {{v}_{oy}}=\left( \frac{531}{\sin 2\theta } \right)\sin \theta \\ & \\ & {{v}_{ox}}=\left( \frac{531}{\sin 2\theta } \right)\cos \theta \\ \end{align}\ \)

b)

\(\begin{align} & y={{y}_{0}}+{{v}_{oy}}t-\frac{g{{t}^{2}}}{2} \\ & 3,1=0+{{v}_{oy}}4-\frac{9,8\cdot 16}{2} \\ & 3,1+78,4=4{{v}_{oy}} \\ & {{v}_{oy}}=20,3m/s \\ & \\ & x={{x}_{0}}+{{v}_{ox}}t \\ & 54,5=0+{{v}_{ox}}4 \\ & {{V}_{ox}}=13,6m/s \\ & \\ & v=\sqrt{{{20,3}^{2}}+{{13,6}^{2}}} \\ & v=\sqrt{412+185} \\ & v=24,4m/s \\ \end{align}\ \)

c) 

\(\begin{align} & v={{v}_{ox}}\cos \theta \\ & 24,4=13,6\cos \theta \\ & \cos \theta =\frac{24,4}{13,6} \\ & \cos \theta =1,79 \\ & \theta =37,8{}^\text{o} \\ \end{align}\ \)

d) 

\(\begin{align} & H=\frac{{{v}^{2}}{{\sin }^{2}}\theta }{2g} \\ & H=\frac{{{24,4}^{2}}{{\sin }^{2}}37,8}{2\cdot 9,8} \\ & H=\frac{595,36\cdot 0,37}{19,6} \\ & H=11,23m \\ \end{align}\ \)