Question

A projectile 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)

Answer 1

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