(a) The stone travels a vertical distance <em>y</em> of
<em>y</em> = (12.0 m/s) <em>t</em> + 1/2 <em>g t</em> ²
where <em>g</em> = 9.80 m/s² is the acceleration due to gravity. Note that this equation assume the downward direction to be positive, and that <em>y</em> = 0 corresponds to the height from which the stone is thrown.
So if it reaches the ground in <em>t</em> = 1.54 s, then the height of the building <em>y</em> is
<em>y</em> = (12.0 m/s) (1.54 s) + 1/2 (9.80 m/s²) (1.54 s)² ≈ 30.1 m
(b) The stone's (downward) velocity <em>v</em> at time <em>t </em>is
<em>v</em> = 12.0 m/s + <em>g t</em>
so that after <em>t</em> = 1.54 s, its velocity is
<em>v</em> = 12.0 m/s + (9.80 m/s²) (1.54 s) ≈ 27.1 m/s
(and of course, speed is the magnitude of velocity)
