Answer
(a) 13.4 m/s
(b) 1.37 s
Work Step by Step
Please see the attached image first.
(a) To find the velocity of the diver, we can apply the equation $V^{2}=U^{2}+\space 2aS$ as follows,
$\downarrow\space V^{2}=U^{2}+\space 2aS $
Let's plug known values into this equation,
$V^{2}=0^{2}+\space 2\times9.8\space m/s^{2}\times 9.21\space m$
$V^{2}=180.5\space m^{2}/s^{2}$
$V\space\space= \sqrt{180.5\space m^{2}/s^{2}}$
$V\space\space=13.4\space m/s$
The water entering speed of the diver = 13.4 m/s
(b) To find the diver's fly time in the air, we can apply the equation $V=U+at$ as follows,
$\downarrow V=U+at$
Let's plug known values into this equation,
$13.4\space m/s=0+9.8\space m/s^{s}\times t$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space t=\frac{13.4\space m/s}{9.8\space m/s^{2}}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space t=1.37\space s$
