The velocities at time t are
• Horizontal:
v = (30.0 m/s) cos(20.0º)
• Vertical:
v = (30.0 m/s) sin(20.0º) - g t
(where g = 9.80 m/s² is the magnitude of the acceleration due to gravity)
If you only want the initial velocities, they are
• Horizontal:
v = (30.0 m/s) cos(20.0º) ≈ 28.2 m/s
• Vertical:
v = (30.0 m/s) sin(20.0º) ≈ 10.3 m/s
(just set t = 0)
As far as starting equations go, you can derive everything from the definition for average acceleration:
a = ∆v / ∆t = (final v - initial v) / t
→ v = u + a t
(here, u stands in for "initial v" and v is simply velocity at time t )
There is no acceleration in the horizontal direction, while the ball is essentially in free-fall in the vertical direction.
