[tex]\displaystyle \text{Se da:}\\ \\
h_1=\frac h2\\ \\
v_1=20\frac ms\\ \\
t=?s\\ \\ \\
\text{Formule:}\\ \\
\text{Avem de aface cu o cadere, fara viteza initiala, deci:}\\ \\ \\
h=\frac{g\times t^2}{2}\\ \\ \\[/tex]
[tex]\displaystyle \text{De unde:}\\ \\ \\
t=\sqrt\frac{2\times h}{g}\\ \\ \\
\text{Aflam h din formula lui Galilei pentru cadere fara viteza initiala:}\\ \\ \\
v_1^2=2\times g\times h_1\\ \\
v_1^2=2\times g\times \frac h2\\ \\
v_1^2=g\times h\\ \\
h=\frac{v_1^2}{g},\text{ se putea afla prin conservarea energiilor}\\ \\ \\[/tex]
[tex]\displaystyle \text{Inlocuim si obtinem:}\\ \\ \\
t=\sqrt\frac{2\times v_1^2}{g^2}\\ \\ \\
\boxed{t=\frac vg\times\sqrt2}\\ \\ \\
\text{Calcule:}\\ \\
t=\frac {20}{10}\times\sqrt2\approx 2,83s
[/tex]
