The working formula to analyze this problem is
Vf^2 - Vo^2 = 2gs
where
Vf = velocity at which the gymnast hits the ground
Vo = initial velocity of the gymnast (given as 4 m/s and -3 m/s)
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
s = height at which gymnast starts her dismount
For the first dismount,
Vf^2 - (4)^2 = 2(9.8)(s)
Vf^2 = 16 + 19.6s
and for the second dismount,
Vf^2 - (-3)^2 = 2(9.8)(s)
Vf^2 = 9 + 1.6s
Since "s" is the same for both dismounts, then her final velocity in the first dismount is higher than that of her second dismount.
