The initial speed of the arrow is 15 m/s and the arrow is shot from the top of a 30 m cliff. The height at which the arrow moves downward at a speed of 8 m/s can be calculated using the equation of motion:
H = 30 + (15^2 - 8^2) / (2 * 9.8)
H = 30 + (225 - 64) / 19.6
H = 30 + 161 / 19.6
H = 30 + 8.2
H = 38.2 m
Therefore, the height at which the arrow moves downward at a speed of 8 m/s is 38.2 m.