Answer
$(a)\space 32\space s$
$(b)\space 3\space miles\space or\space 5\space km$
Work Step by Step
Please see the attached image first
Let's apply the equation $V=U+at$ to find the time taken to reach the speed of sound.
$\downarrow\space V=U+at$
Let's plug known values into this equation.
$311\space m/s = 0+(9.7\space m/s^{2})\space t$
$t=32\space s$
So, he falls 32 s to reach the speed of the sound.
(b) Let's apply the equation $V^{2}=U^{2}+2aS$ to find the displacement of skydriver.
$\downarrow V^{2}=U^{2}+2aS$
Let's plug known values into this equation.
$\space \space \space (311\space m/s)^{2}=(0)^{2}+2\times(9.7\space m/s^{2})\times h$
$96721\space m^{2}/s^{2}=19.4h\space m/s^{2}$
$h=4985.6\space m\approx 5\space km\space or\space 3\space miles$
So, he falls 3 miles to reach the speed of sound.
