A ball is released from a height \(h\). If \(t_{1}\) and \(t_{2}\) be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between \(t_{1}\) and \(t_{2}\).

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(t _{2}=(\sqrt{2}-1) t _{1}\)

Detailed explanation

For first \(\frac{ h }{2}\)

\(\frac{ h }{2}=\frac{1}{2} gt _{1}^{2}\)

For total height \(h\)

\(h =\frac{1}{2} g \left( t _{1}+ t _{2}\right)^{2}\)

\(\frac{1}{\sqrt{2}}=\frac{ t _{1}}{ t _{1}+ t _{2}}\)

\(1+\frac{ t _{2}}{ t _{1}}=\sqrt{2}\)

\(\frac{ t _{1}}{ t _{2}}=\frac{1}{\sqrt{2}-1}\)

\(t _{2}=(\sqrt{2}-1) t _{1}\)

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