I.
a) f = F
[tex]f = mg[/tex]
wyznaczam m
[tex]m = \frac{f}{g} [/tex]
wyznaczam g
[tex]g = \frac{f}{m} [/tex]
b)
[tex]d = \frac{m}{v} [/tex]
wyznaczam m
[tex]m = dv[/tex]
wyznaczam v
[tex]dv = m[/tex]
[tex]v = \frac{m}{d} [/tex]
c)
[tex]p = dgh[/tex]
wyznaczam d
[tex]dgh = p[/tex]
[tex]d = \frac{p}{gh} [/tex]
wyznaczam g
[tex]dgh = p[/tex]
[tex]g = \frac{p}{dh} [/tex]
wyznaczam h
[tex]dgh = p[/tex]
[tex]h = \frac{p}{dg} [/tex]
II.
[tex]e = \frac{1}{2} m {v}^{2} + mgh[/tex]
e = E
a) wyznaczam g
[tex] \frac{1}{2} m {v}^{2} + mgh = e[/tex]
[tex]mgh = e - \frac{1}{2} m {v}^{2} [/tex]
[tex]g = \frac{e - \frac{1}{2}m {v}^{2} }{mh} [/tex]
b) wyznaczam v
[tex] \frac{1}{2} m {v}^{2} + mgh = e[/tex]
[tex] \frac{1}{2} m {v}^{2} = e - mgh[/tex]
[tex]m {v}^{2} = 2e - 2mgh[/tex]
[tex] {v}^{2} = \frac{2e - 2mgh}{m} [/tex]
[tex]v = \sqrt{ \frac{2e - 2mgh}{m} } [/tex]
