Answer:
5.55935324 m
Explanation:
r = Radius = 4 m
h = Height = 6 m
Frequency is
[tex]f=\frac{1}{T}\\\Rightarrow f=\frac{1}{5}\ Hz[/tex]
Angular speed is given by
[tex]\omega=2\pi f\\\Rightarrow \omega=\frac{2}{5}\pi[/tex]
Tangential velocity of the hat is given by
[tex]v=r\omega\\\Rightarrow v=4\times\frac{2}{5}\pi\\\Rightarrow v=5.02654\ m/s[/tex]
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
g = Acceleration due to gravity = 9.81 m/s²
From equation of motion
[tex]s=ut+\frac{1}{2}gt^2\\\Rightarrow 6=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{6\times 2}{9.81}}\\\Rightarrow t=1.106\ s[/tex]
Distance = Speed×Time
[tex]Distance=5.02654\times 1.106=5.55935324\ m[/tex]
The hat will land 5.55935324 m away from the point of release
