• Velocidade das velas
[tex3]S=S_0+vt [/tex3]
[tex3]h=v_1t_1\ \therefore \ \boxed{v_1 =\frac{h}{t_1}} [/tex3]
Analogamente:
[tex3]\boxed{v_2=\frac{h}{t_2}} [/tex3]
• Velocidade das sombras:
• Considerando [tex3]v_2> v_1 [/tex3]
:
[tex3]• \text{ Sombra 2:} [/tex3]
- IMG_20200107_000338983.jpg (15.97 KiB) Exibido 2579 vezes
[tex3]\frac{a}{2a} =\frac{∆S_2-∆S_1}{∆S_{sombra_2}-∆S_1}[/tex3]
[tex3]\frac 12 = \frac{\frac{h}{t_2}\cdot t-\frac{h}{t_1}\cdot t}{v_{sombra_2}\cdot t-\frac{h}{t_1}\cdot t} [/tex3]
[tex3]v_{sombra_2}-\frac{h}{t_1}= \frac{2h}{t_2}-\frac{2h}{t_1} [/tex3]
[tex3]v_{sombra_2}=\frac{2h}{t_2}-\frac{h}{t_1} [/tex3]
[tex3]\boxed{\boxed{v_{sombra_2}=h\cdot \(\frac{ 2t_1-t_2}{t_1\cdot t_2}\)}}[/tex3]
[tex3]•\text{ Sombra 1:} [/tex3]
- IMG_20200107_000352905.jpg (17.14 KiB) Exibido 2579 vezes
[tex3]\frac{∆S_2}{∆S_1}=\frac{2a+x}{a+x}[/tex3]
[tex3]\frac{\frac{h}{t_2}\cdot t}{\frac{h}{t_1}\cdot t}=\frac{2a+x}{a+x} [/tex3]
[tex3]\frac{t_1}{t_2}=\frac{2a+x}{a+x}[/tex3]
[tex3]at_1+xt_1= 2at_2+xt_2[/tex3]
[tex3]\boxed{ x=\frac{a(2t_2-t_1)}{t_1-t_2}}[/tex3]
[tex3]\frac{∆S_{sombra_1}}{∆S_1}=\frac{x}{a+x}[/tex3]
[tex3]\frac{v_{sombra_1}\cdot t}{\frac{h}{t_1}\cdot t}=\frac{\frac{a(2t_2-t_1)}{t_1-t_2}}{a+\frac{a(2t_2-t_1)}{t_1-t_2}} [/tex3]
[tex3]\frac{v_{sombra_1}}{\frac{h}{t_1}}=\frac{ \frac{2t_2-t_1}{t_1-t_2}}{\frac{t_2}{t_1-t_2}}[/tex3]
[tex3]\boxed{\boxed{ v_{sombra_1}=h\cdot \(\frac{2t_2-t_1}{t_1\cdot t_2}\)}}[/tex3]
