Tóm tắt:
$m=1\,\,\left( kg \right)$
$v=20\,\,\left( m/s \right)$
$h=20\,\,\left( m \right)$
$g=10\,\,\left( m/{{s}^{2}} \right)$
………………………
a)
${{W}_{d}}=\dfrac{1}{2}m{{v}^{2}}=\dfrac{1}{2}{{.1.20}^{2}}=\,200\,\,\left( J \right)$
${{W}_{t}}=mgh=1.10.20=200\,\,\left( J \right)$
$W={{W}_{d}}+{{W}_{t}}=200+200+400\,\,\left( J \right)$
b)
$\,\,\,\,\,\,{{W}_{t\max }}=W$
$\to mg{{h}_{\max }}=400$
$\to {{h}_{\max }}=\dfrac{400}{mg}$
$\to {{h}_{\max }}=\dfrac{400}{1.10}=40\,\,\left( m \right)$
c)
${{W}_{t}}=3{{W}_{d}}$
Theo định luật bảo toàn cơ năng
$\,\,\,\,\,\,{{W}_{t}}+{{W}_{d}}=W$
$\to 3{{W}_{d}}+{{W}_{d}}=W$
$\to 4{{W}_{d}}=W$
$\to 4.\dfrac{1}{2}m{{v}^{2}}=400$
$\to 4.\dfrac{1}{2}.1.{{v}^{2}}=400$
$\to {{v}^{2}}=200$
$\to v=10\sqrt{2}\,\,\left( m/s \right)$