The 'spot' at the end of the laser beam moves in a circle. The radius of the circle is the distance between the laser and the spot.
The circumference of every circle is (2π) · (radius) .
The speed of the spot is (distance) / (time) .
Speed = (circumference) / (time to turn once around the full circle)
Speed =
(circumference) · (nr of revs) / (second) .
(a). Speed = (2π) (8km) · (9 rev) / sec
Speed = (2π · 8 · 9) km/sec
Speed = 144π km/sec
Speed = 452.4 km/sec
(b). Speed = (2π) (16km) · (9 rev) / sec
Speed = (2π · 16 · 9) km/sec
Speed = 288π km/sec
Speed = 904.8 km/sec
(c). 300,000 km/sec = (2π · distance) · (9 / sec)
300,000 km = (18π · distance)
Distance = 300,000 / 18π km
Distance = 5,305 km