To solve this problem we will use the relationship given between the centripetal Force and the Force caused by the weight, with respect to the horizontal and vertical components of the total tension given.
The tension in the vertical plane will be equivalent to the centripetal force therefore
[tex]Tsin\theta= \frac{mv^2}{r}[/tex]
Here,
m = mass
v = Velocity
r = Radius
The tension in the horizontal plane will be subject to the action of the weight, therefore
[tex]Tcos\theta = mg[/tex]
Matching both expressions with respect to the tension we will have to
[tex]T = \frac{\frac{mv^2}{r}}{sin\theta}[/tex]
[tex]T = \frac{mg}{cos\theta}[/tex]
Then we have that,
[tex]\frac{\frac{mv^2}{r}}{sin\theta} = \frac{mg}{cos\theta}[/tex]
[tex]\frac{mv^2}{r} = mg tan\theta[/tex]
Rearranging to find the velocity we have that
[tex]v = \sqrt{grTan\theta}[/tex]
The value of the angle is 14.5°, the acceleration (g) is 9.8m/s^2 and the radius is
[tex]r = \frac{\text{diameter of rotational circular platform}}{2} + \text{length of chains}[/tex]
[tex]r = \frac{11.1}{2}+2.41[/tex]
[tex]r = 7.96m[/tex]
Replacing we have that
[tex]v = \sqrt{(9.8)(7.96)tan(14.5\°)}[/tex]
[tex]v = 4.492m/s[/tex]
Therefore the speed of each seat is 4.492m/s
