Answer:
5 m/s
Step-by-step explanation:
Horizontal distance traveled, x = 2 m
vertical distance traveled, y = 4/5 m
Let the speed of cup as it leaves the counter is v and it takes time t to hit the ground.
Use second equation of motion in vertical direction

Here acceleration in vertical direction is 9.8 m/s^2.
So,

t = 0.4 second
Now in horizontal direction the acceleration in zero.
Horizontal distance = horizontal velocity x time
x = v t
2 = v (0.4)
v = 5 m/s
Thus, the horizontal velocity of cup as it leaves the counter is 5 m/s.