Answer:
[tex]v_0 = v(t)+gt[/tex]
Explanation:
The vertical velocity of an object in free fall is given by:
[tex]v(t) = v_0 +at[/tex]
where
v0 is the initial vertical velocity
a is the acceleration, which actually corresponds to [tex]g=-9.8 m/s^2[/tex] (gravitational acceleration, with downward direction)
t is the time
So the explicit formula would be
[tex]v(t) = v_0 +gt[/tex]
And we can re-write it to find the initial vertical velocity:
[tex]v_0 = v(t)-gt[/tex]
For our problem, we have
v(t) = -6.5 m/s (with negative sign since the ball is falling downward)
t = 1.5 s
Substituting, we find
[tex]v_0 = -6.5 m/s -(-9.8 m/s^2)(1.5 s)=8.2 m/s[/tex]
in the upward direction.
