Chọn gốc thế năng tại mặt đất:
a)
$\,\,\,\,\,\,\,W={{W}_{đ\max }}$
$\to \dfrac{1}{2}m{{v}^{2}}+mgh=\dfrac{1}{2}mv_{\max }^{2}$
$\to {{v}^{2}}+2gh=v_{\max }^{2}$
$\to {{20}^{2}}+2.10.h={{30}^{2}}$
$\to h=25\,\,\left( m \right)$
b)
$\,\,\,\,\,\,\,{{W}_{t\max }}={{W}_{đ\max }}$
$\to mg{{h}_{\max }}=\dfrac{1}{2}mv_{\max }^{2}$
$\to 2g{{h}_{\max }}=v_{\max }^{2}$
$\to 2.10.{{h}_{\max }}={{30}^{2}}$
$\to {{h}_{\max }}=45\,\,\,\left( m \right)$
c)
${{W}_{đ}}=3{{W}_{t}}\to {{W}_{t}}=\dfrac{1}{3}{{W}_{đ}}$
$\,\,\,\,\,\,\,{{W}_{đ}}+{{W}_{t}}=W$
$\to {{W}_{đ}}+\dfrac{1}{3}{{W}_{đ}}=W$
$\to 4{{W}_{đ}}=3W$
$\to 4.\dfrac{1}{2}m{{v}^{2}}=3mg{{h}_{\max }}$
$\to 2{{v}^{2}}=3g{{h}_{\max }}$
$\to 2{{v}^{2}}=3.10.45$
$\to v=15\sqrt{3}\,\,\,\left( m/s \right)$
