Hi there!
(A)
When the rock reaches the peak, it will have a vertical velocity of 0 m/s. We can use the equation:
vf = vi + at
vf = final velocity (0 m/s)
vi = initial velocity (2 m/s)
a = acceleration (in this situation, due to gravity = 9.8 m/s²)
t = time (s)
0 = 2 + (-9.8)t
2/9.8 = t = .204 sec
(B)
Use the equation:
d = vit + 1/2at²
d = 2(.204) + 1/2(-9.8)(.204²)
d = .204 m