Sam tosses a ball horizontally off a footbridge at 4.8 m/s. How much time passes after he releases it until its speed doubles?

When the speed has doubled, the vertical component of speed will be

sqrt[(9.6)^2 - (4.8)^2] = 8.31 m/s
(The horizontal velocity component will remain 4.8 m/s.)

The time needed to attain that vertical velocity component is
t = (8.31 m/s)/g = 0.848 seconds