Respuesta :
Answer:
The angular velocity is 15.37 rad/s
Solution:
As per the question:
[tex]\theta = 54.6^{\circ}[/tex]
Horizontal distance, x = 30.1 m
Distance of the ball from the rotation axis is its radius, R = 1.15 m
Now,
To calculate the angular velocity:
Linear velocity, v = [tex]\sqrt{\frac{gx}{sin2\theta}}[/tex]
v = [tex]\sqrt{\frac{9.8\times 30.1}{sin2\times 54.6}}[/tex]
v = [tex]\sqrt{\frac{9.8\times 30.1}{sin2\times 54.6}}[/tex]
v = [tex]\sqrt{\frac{294.98}{sin109.2^{\circ}}} = 17.67\ m/s[/tex]
Now,
The angular velocity can be calculated as:
[tex]v = \omega R[/tex]
Thus
[tex]\omega = \frac{v}{R} = \frac{17.67}{1.15} = 15.37\ rad/s[/tex]
