Answer:
(a) 33.3 rad/s
(b) 500 N
(c) 40.8 m
Explanation:
Angular velocity [tex]\omega[/tex] is given by
[tex]\omega=\frac {v}{r}[/tex]
Where v is linear velocity and r is radius of circle
[tex]\omega=\frac {35 m/s}{1.05m}=33.3 rad/s[/tex]
Angular velocity is 33.3 rad/s
(b)
Velocity, v is calculated as
[tex]V=\frac {r}{t}[/tex] where r is radius of circle and t is time
Making r the subject of the formula
r=vt
In this case, t=20 ms converted to seconds will be 20/1000=0.02 s
r=20*0.02=0.4m
Force, [tex]F=ma_{c}[/tex] where m is mass and [tex]a_{c}[/tex] is centripetal acceleration
[tex]a_{c}=\frac {v^{2}}{r}[/tex]
Therefore
[tex]F=m\frac {v^{2}}{r}[/tex]
[tex]F=05\frac {20^{2}}{0.4}=500N[/tex]
Force=500 N
(c)
Maximum range covered by the football
[tex]d=\frac {v^{2}}{g}sin(2\theta)[/tex] where g is gravitational constant taken as 9.8, [tex]\theta[/tex] is 45 and v is 20 m/s
[tex]d=\frac {20^{2}}{9.8}sin((2)(45))=40.8 m[/tex]
Maximum range covered is 40.8 m
