A child on a merry-go-round is moving with a speed of 1.40 m/s when 1.18 m from the center of the merry-go-round.

(a) Calculate the centripetal acceleration of the child.

(b) Calculate the net horizontal force exerted on the child (mass = 25.0 kg).

I will be happy to critique your work.

well for a) I got 1.08m/s^2

To calculate the centripetal acceleration of the child on the merry-go-round, we can use the formula:

a = v^2 / r

where:
a is the centripetal acceleration
v is the linear velocity of the child
r is the radius of the merry-go-round

In this case, the linear velocity of the child is given as 1.40 m/s and the distance from the center of the merry-go-round (which is equal to the radius) is given as 1.18 m.

(a) calculating centripetal acceleration:
a = (1.40 m/s)^2 / 1.18 m
a = 1.96 m^2/s / 1.18 m
a ≈ 1.66 m/s^2

Therefore, the centripetal acceleration of the child is approximately 1.66 m/s^2.

To calculate the net horizontal force exerted on the child, we can use Newton's second law:

F = m * a

where:
F is the net force exerted on the child
m is the mass of the child
a is the centripetal acceleration

In this case, the mass of the child is given as 25.0 kg and the centripetal acceleration was calculated to be approximately 1.66 m/s^2.

(b) calculating net horizontal force:
F = 25.0 kg * 1.66 m/s^2
F ≈ 41.5 N

Therefore, the net horizontal force exerted on the child is approximately 41.5 Newtons.