Final answer:
To find the child's centripetal acceleration, we use the formula a = rω². With the given radius of 1.35 m and an angular speed of 4.62 rad/s, the centripetal acceleration is 28.815 m/s².
Step-by-step explanation:
The child's centripetal acceleration on a merry-go-round can be calculated using the formula for centripetal acceleration: a = rω², where r is the radius and ω is the angular speed. Since the radius is given as 1.35 m and the angular speed is 4.62 rad/s, the calculation will be: a = (1.35 m) × (4.62 rad/s)². Plugging in the values, we get a = 1.35 m × 21.3444 rad²/s², which equals approximately 28.815 m/s².