Explanation

(a) From equation of motion, we have
$h = ut + \frac{1}{2}gt^{2}$
taking upward direction as negative and downward direction as positive, we have
$\ \ \ \ \ \ \ \ \ \ \ \ \ h = 65\ m,$
$\ \ \ \ \ \ \ \ \ \ \ \ \ u = - 12\ {ms}^{- 1}and\ g = 10\ {ms}^{- 2}$
$\therefore\ \ \ \ \ \ \ 65 = - 12t + \frac{1}{2} \times 10 \times t^{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ 5t^{2} - 12t - 65 = 0$
$\Rightarrow \ \ \ \ \ \ \ \ (t - 5)(5t + 13) = 0$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t = 5\ s$
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