Đáp án:
\(\begin{array}{l}
a.{v_{\max }} = 20\sqrt 3 m/s\\
b.h = 20m\\
v = 20\sqrt 2 m/s\\
c.h = 40m
\end{array}\)
Giải thích các bước giải:
a.
Bảo toàn cơ năng;
\(\begin{array}{l}
{W_{t\max }} = {W_{d\max }} \Rightarrow mg{h_{\max }} = \frac{1}{2}mv_{\max }^2\\
\Rightarrow 10.60 = \frac{1}{2}.v_{\max }^2 \Rightarrow {v_{\max }} = 20\sqrt 3 m/s
\end{array}\)
b.
Ta có:
\(\begin{array}{l}
{W_d} = 2{W_t} \Rightarrow {W_t} = \frac{W}{3} \Rightarrow mgh = \frac{{mg{h_{\max }}}}{3}\\
\Rightarrow h = \frac{{{h_{\max }}}}{3} = \frac{{60}}{3} = 20m\\
{W_d} = 2{W_t} \Rightarrow \frac{1}{2}m{v^2} = mgh \Rightarrow \frac{1}{2}.{v^2} = 2.10.20\\
\Rightarrow v = 20\sqrt 2 m/s
\end{array}\)
c.
Ta có:
\(\begin{array}{l}
{W_t} = 2{W_d} \Rightarrow {W_t} = \frac{{2W}}{3} \Rightarrow mgh = \frac{{2.mg{h_{\max }}}}{3}\\
\Rightarrow h = \frac{{2{h_{\max }}}}{3} = \frac{{2.60}}{3} = 40m
\end{array}\)
