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