Question

PRECISO MUITO DE AJUDA, É URGENTE

Answer 1

Vamos usar a Conservação de Energia Mecânica.

Lembrando que $\textsf{E}_\textsf{M} = \textsf{E}_\textsf{P} + \textsf{E}_\textsf{C}$ e que $\textsf{E}_\textsf{Mi} = \textsf{E}_\textsf{Mf}$.

a)

$\textsf{E}_\textsf{Mi} = \textsf{E}_\textsf{Mf}\\\\\textsf{E}_\textsf{Pi} + \textsf{E}_\textsf{Ci} = \textsf{E}_\textsf{Pf} + \textsf{E}_\textsf{Cf}\\\\\textsf{E}_\textsf{Pi} = \textsf{E}_\textsf{Pf} + \textsf{E}_\textsf{Cf}\\\\mgH = mgh + \frac{1}{2}mv^2\\\\mgH = m(gh + \frac{1}{2}v^2)\\\\gH = gh + \frac{1}{2}v^2\\\\\frac{1}{2}v^2 = gH- gh\\\\v^2 = 2g(H- h)\\\\v = \sqrt{ 2g(H- h)}\\v = \sqrt{2\times10\times(8-4)}\\v = \sqrt{80}\\\\\boxed{v = 4\sqrt{5} \textsf{ m/s}}$

b)

$\textsf{E}_\textsf{Pi} + \textsf{E}_\textsf{Ci} = \textsf{E}_\textsf{Pf} + \textsf{E}_\textsf{Cf}\\\\\textsf{E}_\textsf{Pi} = \textsf{E}_\textsf{Cf}\\\\mgH =\frac{1}{2}mv^2\\\\gH = \frac{1}{2}v^2\\\\\frac{1}{2}v^2 = gH\\\\v^2 = 2gH\\v = \sqrt{ 2gH}\\v = \sqrt{2\times10\times8}\\v = \sqrt{160}\\\\\boxed{v = 4\sqrt{10} \textsf{ m/s}}$