First we can find the swimmer's velocity when the feet enter the water.
v^2 = (v0)^2 + 2gy
v = sqrt{ (v0)^2 + 2gy }
v = sqrt{ (4.00 m/s)^2 + (2)(-9.80 ~m/s^2)(-8 m) }
v = sqrt{ 172.8 }
v = -13.145 m/s
Note that the negative sign means the swimmer is moving downward.
We can find the time to reach this velocity.
t = (v - v0) / g
t = (-13.145 m/s - 4.00 m/s)) / -9.80 m/s^2
t = - 17.145 m/s / -9.80 m/s^2
t = 1.75 seconds
Her feet are in the air for 1.75 seconds.
