A ballplayer catches a ball 3.0s after throwing it vertically upward. With what speed did he throw it, and what height did it reach?

We can find final velocity using the equation as follows:

vf = vi + g*t

Substituting our known values for vi and g we obtain:

vf = vi + g*t

vf = 0 + (9.8) * (1.5) [ 1.5 s since it is the time it take to reach the top and to fall back)

vf = 14.7 = 15m/s

We can find the distance traveled using

d = vi*t + 1/2g*t^2

Substituting our values for vi, g and t we get

d = 0 * (1.5) + (1/2) * (9.8) * (1.5) ^2

d = 11m