A child sitting 1.08 m from the center of a merry-go-round moves with a speed of 1.20 m/s.
(a) Calculate the centripetal acceleration of the child.
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centripetal acceleration is v^2/r where v is velocity and r is radius. so, 1.20^2/1.08 which is 1.33
To calculate the centripetal acceleration of the child, we need to use the formula:
a = v^2 / r
where:
a is the centripetal acceleration,
v is the velocity of the child, and
r is the radius of the circular path.
In this case, we are given that the child's velocity is 1.20 m/s and the child is sitting 1.08 m from the center of the merry-go-round.
Substituting the given values into the formula, we get:
a = (1.20 m/s)^2 / 1.08 m
Simplifying the equation, we have:
a = 1.44 m^2/s^2 / 1.08 m
Dividing, we find:
a ≈ 1.33 m/s^2
Therefore, the centripetal acceleration of the child is approximately 1.33 m/s^2.