Answer:
No, the ball will not clear the fence.
Solution:
Angular velocity, ![\omega = 70\ rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%2070%5C%20rad%2Fs)
Height, h = 1.2 m
Angle, ![\theta = 45^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2045%5E%7B%5Ccirc%7D)
Distance covered by the ball, d = 110 m
Length of the fence, l = 1.2 m
Radius of the axis, R = 46 cm = 0.46 m
Now,
To calculate the linear velocity of the ball, v:
![v = \omega R = 70\times 0.46 = 32.2\ m/s](https://tex.z-dn.net/?f=v%20%3D%20%5Comega%20R%20%3D%2070%5Ctimes%200.46%20%3D%2032.2%5C%20m%2Fs)
Total time taken:
![t = \frac{2vsin\theta}{g} = \frac{2\times 32.2sin45^{\circ}}{9.8} = 4.646\ s](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B2vsin%5Ctheta%7D%7Bg%7D%20%3D%20%5Cfrac%7B2%5Ctimes%2032.2sin45%5E%7B%5Ccirc%7D%7D%7B9.8%7D%20%3D%204.646%5C%20s)
The distance at which the ball falls, with a = 0 is given by:
![x = vt + \frac{1}{2}at^{2} = 32.2cos45^{\circ}\times 4.646 = 105.78\ m](https://tex.z-dn.net/?f=x%20%3D%20vt%20%2B%20%5Cfrac%7B1%7D%7B2%7Dat%5E%7B2%7D%20%3D%2032.2cos45%5E%7B%5Ccirc%7D%5Ctimes%204.646%20%3D%20105.78%5C%20m)
Since, the ball has to clear a fence 1.2 m long and a t a distance 110 m away, clearly it will not be able to cross it.