${\displaystyle \mathrm {sen} \,\theta ={\dfrac {3}{5}}\qquad \cos \theta ={\dfrac {4}{5}}\qquad \qquad \qquad \mathrm {sen} \,\alpha ={\dfrac {4}{5}}\qquad \cos \alpha ={\dfrac {3}{5}}.}$

${\displaystyle {\begin{array}{l}{\vec {r}}(0)={\vec {0}}\\{\vec {v}}(0)=10v_{p}\cos \alpha \,{\vec {\imath }}+10v_{p}\,\mathrm {sen} \,\alpha \,{\vec {\jmath }}=6v_{p}\,{\vec {\imath }}+8v_{p}\,{\vec {\jmath }}.\end{array}}}$

${\displaystyle {\begin{array}{l}{\vec {a}}=-g\,{\vec {\jmath }},\\{\vec {v}}=6v_{p}\,{\vec {\imath }}+(8v_{p}-gt)\,{\vec {\jmath }},\\{\vec {v}}=6v_{p}t\,{\vec {\imath }}+(8v_{p}t-gt^{2}/2)\,{\vec {\jmath }},\\\end{array}}}$

${\displaystyle {\overrightarrow {OA}}=l\cos \theta \,{\vec {\imath }}+l\,\mathrm {sen} \,\theta \,{\vec {\jmath }}={\dfrac {4}{5}}l\,{\vec {\imath }}+{\dfrac {3}{5}}l\,{\vec {\jmath }}.}$

${\displaystyle {\overrightarrow {OA}}={\vec {r}}(t_{i})\Longrightarrow \left\{{\begin{array}{l}{\dfrac {4}{5}}l=6v_{p}t_{i}\\\\{\dfrac {3}{5}}l=8v_{p}t_{i}-{\dfrac {1}{2}}gt_{i}^{2}\end{array}}\right.}$

${\displaystyle t_{A}={\dfrac {v_{p}}{g}},\qquad l={\dfrac {105}{2}}{\dfrac {v_{p}^{2}}{g}}.}$

${\displaystyle \Delta W_{g}=-\Delta U_{g}=-mgl\,\mathrm {sen} \,\theta =-{\dfrac {63}{2}}mv_{p}^{2}.}$

${\displaystyle P_{g}={\vec {F}}_{g}\cdot {\vec {v}}=m{\vec {g}}\cdot {\vec {v}}=-g(8v_{p}-gt)}$

${\displaystyle {\begin{array}{l}{\vec {v}}_{i}={\vec {v}}_{p}(t_{i})=6v_{p}\,{\vec {\imath }}-7v_{p}\,{\vec {\jmath }}\\{\vec {a}}_{i}=-g\,{\vec {\jmath }}.\end{array}}}$

${\displaystyle |{\vec {v}}_{i}|={\sqrt {85}}\,v_{p}.}$

${\displaystyle a_{T}={\dfrac {{\vec {a}}_{i}\cdot {\vec {v}}_{i}}{|{\vec {v}}_{i}|}}=-{\dfrac {7}{\sqrt {85}}}g.}$

${\displaystyle a_{N}={\dfrac {|{\vec {a}}_{i}\times {\vec {v}}_{i}|}{|{\vec {v}}_{i}|}}={\sqrt {|{\vec {a}}_{i}|^{2}-a_{T}^{2}}}={\dfrac {6}{\sqrt {85}}}\,g.}$