For every complete revolution the boy makes around the center of the carousel, he travels a distance of 2π (5.0 m) = 10π m, which gives a linear speed of
v = (10π m) / (8.0 s) ≈ 3.927 m/s
Then his centripetal acceleration would be
a = v ² / (5.0 m) ≈ 3.084 m/s²
so that the centripetal force exerted on him has magnitude
F = (45 kg) a ≈ 138.791 N ≈ 140 N
(rounded to 2 significant digits)
