Aprojectile is shot straight upward from the earth with a speed of 20 m/s. how high is it when its speed is 8.0 m/s? ignore air friction. (hint: the projectile’s energy is conserved)

The first thing you should do for this case is to write the kinematic equations of the object in the vertical direction.
 For this case, we have
 a = -9.8 m / s ^ 2
 Vf = a * t + Vo
 clearing time:
 t = (Vf-Vo) / (a)
 t = ((8) - (20)) / ((- 9.8)) = 1.22 s
 the position of the object for that time and for when V = 8.0 m / s is
 y (t) = a * t ^ 2/2 + Vot + I
 y (1.22) = (- 9.8) * (1.22) ^ 2/2 + (20) (1.22) + 0 = 17.11m
 answer
 the projectile is 17.11m high when its speed is 8.0 m / s

There was no intial y-momentum so the net final y-momentum must also be 0. they can have final velocities in the y-direction