5.
h = 60m
v0 = 40 m/s
[tex]\alpha[/tex] = 30
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v0x = v0 cos [tex]\alpha[/tex] = 40 x [tex]\frac{\sqrt{3}}{2}[/tex] = [tex]20\sqrt{3}[/tex] m/s
v0y = -v0 sin [tex]\alpha[/tex] = -40 x [tex]\frac{1}{2}[/tex] = -20 m/s
Formula lui Galilei
[tex]v^{2} = v_{0}^2 + 2ad[/tex]
Aplicata aici, obtinem:
[tex]v_{y} = \sqrt{v_{0y}^2 + 2gh} = \sqrt{400 + 1200} = \sqrt{1600} = 40[/tex]
De aici, putem calcula viteza finala:
[tex]v^2 = v_{x}^2 + v_{y}^2 = 1200 + 1600 = 2800\\v = \sqrt{2^2\times 7\times 2^2 \times 5^2} = 20\sqrt{7}[/tex]
6.[tex]\tau[/tex] = 0.5s
[tex]t_{0}[/tex] = 2s
Distanta pe care a parcurs-o primul corp este:
[tex]d_1 = v_{0}t + \frac{gt^2}{2} = 0 + \frac{10(2 + 0.5)^2}{2} = 5\times 2.5^2 = 5\times 6.25 = 31.25\:m[/tex]
Distanta pe care a parcurs-o al doilea corp este:
[tex]d_2 = v_{0}t + \frac{gt^2}{2} = 0 + \frac{10(2)^2}{2} = 0 + 20 = 20\:m[/tex]
Diferenta dintre [tex]d_1[/tex] si [tex]d_2[/tex] este distanta dintre ele:
[tex]d_1 - d_2 = 31.25 - 20 = 11.25\:m[/tex]
