Đáp án:
\(\begin{array}{l}
1.\\
{v_{\max }} = 40m/s\\
h = 20m\\
2.\\
{h_{\max }} = 1,25m\\
v = 4,08m/s
\end{array}\)
Giải thích các bước giải:
1.
Bảo toàn cơ năng:
\(\begin{array}{l}
{W_{t\max }} = {W_{d\max }}\\
\Rightarrow mg{h_{\max }} = \dfrac{1}{2}mv_{max}^2\\
\Rightarrow 10.80 = \dfrac{1}{2}.v_{\max }^2\\
\Rightarrow {v_{\max }} = 40m/s
\end{array}\)
Ta có:
\(\begin{array}{l}
{W_d} = 3{W_t}\\
\Rightarrow {W_t} = \dfrac{W}{4} = \dfrac{{{W_{t\max }}}}{4}\\
\Rightarrow mgh = \dfrac{{mg{h_{\max }}}}{4}\\
\Rightarrow h = \dfrac{{{h_{\max }}}}{4} = \dfrac{{80}}{4} = 20m
\end{array}\)
2.
Bảo toàn cơ năng:
\(\begin{array}{l}
{W_{d\max }} = {W_{t\max }}\\
\Rightarrow \dfrac{1}{2}mv_{\max }^2 = mg{h_{\max }}\\
\Rightarrow \dfrac{1}{2}{.5^2} = 10{h_{\max }}\\
\Rightarrow {h_{\max }} = 1,25m
\end{array}\)
Ta có:
\(\begin{array}{l}
{W_d} = 2{W_t}\\
\Rightarrow {W_d} = \dfrac{2}{3}W = \dfrac{{2{W_{t\max }}}}{3}\\
\Rightarrow \dfrac{1}{2}m{v^2} = \dfrac{{2mg{h_{\max }}}}{3}\\
\Rightarrow \dfrac{1}{2}.{v^2} = \dfrac{2}{3}.10.1,25\\
\Rightarrow v = 4,08m/s
\end{array}\)
