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Answer:
the velocity of the kid is 5.6 m/s
Explanation:
r is the radius and w is the frequency.
so we should know that the diameter is 18m and the diameter is equal to two times the radius, so r = 18m/2 = 9m
we should also know that the circumference of a circle is equal to c = 2pi*r, so each revolution has this length. if the kid does 5.9 revolutions in one minute then the kid spins at v = 5.9*2pi*9m/min
so we want to write this in meters per second and this means that we need to divide it by 60!
v = (5.9*2pi*9/60)m/s = 5.56 m/s
so your answer will be 5.6 m/s glad i could help!
0.25 m/s
Explanation:
The radius r of the merry-go-round is half its diameter D:
[tex]r = \frac{1}{2}D = \frac{1}{2}(1.5\:\text{m}) = 0.75\:\text{m}[/tex]
We also need to convert the angular speed from rev/min to rad/s. We know that there are 60 seconds to a minute and that there are [tex]2\pi[/tex] radians per revolution. Therefore,
[tex]\omega = 3.2\:\dfrac{\text{rev}}{\text{min}}×\dfrac{2\pi\:\text{rad}}{1\:\text{rev}}×\dfrac{1\:\text{min}}{60\:\text{s}}[/tex]
[tex]\:\:\:\:=0.335\:\text{rad/s}[/tex]
Now that we know the angular speed in rad/s, the child's linear speed can be calculated as
[tex]v = r\omega = (0.75\:\text{m})(0.335\:\text{rad/s}) = 0.25\:\text{m/s}[/tex]