Đáp án:

\(\begin{array}{l}
a.{h_{\max }} = 8,2m\\
b.{v_{\max }} = 12,8m/s\\
c.h = \dfrac{{82}}{{15}}m
\end{array}\)

Giải thích các bước giải:

a.

Bảo toàn cơ năng:

\(\begin{array}{l}
W = {W_{t\max }}\\
 \Rightarrow mgh + \dfrac{1}{2}m{v^2} = mg{h_{\max }}\\
 \Rightarrow 10.5 + \dfrac{1}{2}{.8^2} = 10{h_{\max }}\\
 \Rightarrow {h_{\max }} = 8,2m
\end{array}\)

b.

Bảo toàn cơ năng:

\(\begin{array}{l}
{W_{t\max }} = {W_{d\max }}\\
 \Rightarrow mg{h_{\max }} = \dfrac{1}{2}mv_{\max }^2\\
 \Rightarrow 10.8,2 = \dfrac{1}{2}.v_{\max }^2\\
 \Rightarrow {v_{\max }} = 12,8m/s
\end{array}\)

c.

Ta có:

\(\begin{array}{l}
{W_t} = 2{W_d} \Rightarrow {W_t} = \dfrac{{2W}}{3} = \dfrac{{2{W_{t\max }}}}{3}\\
 \Rightarrow mgh = \dfrac{{2mg{h_{\max }}}}{3}\\
 \Rightarrow h = \dfrac{2}{3}{h_{\max }} = \dfrac{2}{3}.8,2 = \dfrac{{82}}{{15}}m
\end{array}\)