Answer
See answer below.
Work Step by Step
Equation 1-12:
$v(t_{i+1})=v(t_i)+\left[g-\frac cmv(t_i)\right](t_{i+1}-t_i)$
Computing to t=10s, with $g=9.8\ m/s^2,\ c=12.5\ kg/s,\ m=68.1\ kg, v(0)=0\ m/s$
a) For a step size of 1s
$\begin{array}
{cc}
t_i & v(t_i) \\
\hline
0 &0.00 \\
1 &9.80\\
2 &17.80\\
3 &24.33\\
4 &29.67\\
5 &34.02\\
6 &37.58\\
7 &40.48\\
8 &42.85\\
9 &44.78\\
10 &46.36
\end{array}$
b) For a step size of 0.5s
$\begin{array}
{cc}
t_i & v(t_i) \\
\hline
0.0 &0.00\\
0.5 &4.90\\
1.0 &9.35\\
1.5 &13.39\\
2.0 &17.06\\
2.5 &20.40\\
3.0 &23.43\\
3.5 &26.18\\
4.0 &28.67\\
4.5 &30.94\\
5.0 &33.00\\
5.5 &34.87\\
6.0 &36.57\\
6.5 &38.12\\
7.0 &39.52\\
7.5 &40.79\\
8.0 &41.95\\
8.5 &43.00\\
9.0 &43.95\\
9.5 &44.82\\
10.0 &45.60
\end{array}$
The relative deviation for the final velocity is : $|45.60-46.36|/45.60\times100\%=1.67\%$, which is approximately the improvement in accuracy.
