Answer:
No, the ball will not clear the fence.
Solution:
Angular velocity, [tex]\omega = 70\ rad/s[/tex]
Height, h = 1.2 m
Angle, [tex]\theta = 45^{\circ}[/tex]
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:
[tex]v = \omega R = 70\times 0.46 = 32.2\ m/s[/tex]
Total time taken:
[tex]t = \frac{2vsin\theta}{g} = \frac{2\times 32.2sin45^{\circ}}{9.8} = 4.646\ s[/tex]
The distance at which the ball falls, with a = 0 is given by:
[tex]x = vt + \frac{1}{2}at^{2} = 32.2cos45^{\circ}\times 4.646 = 105.78\ m[/tex]
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.
