I.
a)
m:
[tex]F=mg\qquad|:g\qquad\qquad g\ne0\\\\\dfrac Fg=m\\\\m=\dfrac Fg[/tex]
g:
[tex]F=mg\qquad|:m\qquad\qquad m\ne0\\\\\dfrac Fm=g\\\\g=\dfrac Fm[/tex]
b)
m:
[tex]d=\dfrac mV\qquad|\cdot V\\\\dV=m\\\\m=dV[/tex]
V:
[tex]d=\dfrac mV\qquad|\cdot V\\\\dV=m\qquad|:d\qquad\qquad d\ne0\\\\V=\dfrac md[/tex]
II.
a)
[tex]E=\frac12mv^2+mgh\qquad|-\frac12mv^2\\\\E-\frac12mv^2=mgh\qquad|:(mh)\qquad\qquad m\ne0\,,\ \ h\ne0\\\\\dfrac{E-\frac12mv^2}{mh}=g\\\\g=\dfrac{E-\frac12mv^2}{mh}[/tex]
b)
[tex]E=\frac12mv^2+mgh\qquad|-mgh\\\\E-mgh=\frac12mv^2\qquad|\cdot2\\\\2E-2mgh=mv^2\qquad|:m\qquad\qquad m\ne0\\\\\dfrac{2E}{m}-2gh=v^2\\\\v^2=\dfrac{2E}{m}-2gh\\\\v=\sqrt{\dfrac{2E}{m}-2gh}[/tex]
