Đáp án:

\(\begin{array}{l}
a.{{\rm{W}}_{dA}} = 62,5\left( J \right)\\
{{\rm{W}}_{tA}} = 6250\left( J \right)\\
{\rm{W}} = 6312,5\left( J \right)\\
b.{{\rm{W}}_{dB}} = 1000\left( J \right)\\
{{\rm{W}}_B} = 6312,5\left( J \right)\\
{{\rm{W}}_{tB}} = 5312,5\left( J \right)\\
c.\left\{ \begin{array}{l}
h = 42,1\left( m \right)\\
v = 41,03\left( {m/s} \right)
\end{array} \right.\\
d.{v_c} = 50,25\left( {m/s} \right)
\end{array}\)

Giải thích các bước giải:

chọn mốc thế năng tại mặt đất

\(\begin{array}{l}
a.{{\rm{W}}_{dA}} = \frac{1}{2}mv_A^2 = \frac{1}{2}{.5.5^2} = 62,5\left( J \right)\\
{{\rm{W}}_{tA}} = mg{h_A} = 5.10.125 = 6250\left( J \right)\\
{\rm{W}} = {{\rm{W}}_{tA}} + {{\rm{W}}_{dA}} = 6312,5\left( J \right)\\
b.{v_B} = {v_A} + gt = 5 + 10.3 = 20\left( {m/s} \right)\\
{{\rm{W}}_{dB}} = \frac{1}{2}mv_B^2 = \frac{1}{2}{.5.20^2} = 1000\left( J \right)\\
{{\rm{W}}_B} = {{\rm{W}}_A} = 6312,5\left( J \right)\\
{{\rm{W}}_{tB}} = {{\rm{W}}_B} - {{\rm{W}}_{dB}} = 5312,5\left( J \right)\\
c.\left\{ \begin{array}{l}
{{\rm{W}}_d} = 2{W_t}\\
{{\rm{W}}_d} + {{\rm{W}}_t} = {\rm{W}}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{{\rm{W}}_t} = \frac{{\rm{W}}}{3}\\
{{\rm{W}}_d} = \frac{2}{3}{\rm{W}}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
mgh = \frac{{6312,5}}{3}\\
\frac{1}{2}m{v^2} = \frac{2}{3}.6312,5
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
h = 42,1\left( m \right)\\
v = 41,03\left( {m/s} \right)
\end{array} \right.\\
d.\frac{1}{2}mv_c^2 = {\rm{W}}\\
 \Rightarrow \frac{1}{2}.5.v_c^2 = 6312,5\\
 \Rightarrow {v_c} = 50,25\left( {m/s} \right)
\end{array}\)