Answer:
[tex]s=-38.332m[/tex]
Explanation:
From the question we are told that
Cylinder of mass [tex]m=2.90 kg[/tex]
Radius [tex]R=30.0 m[/tex]
Mass of bucket [tex]M_b= 1.90 kg[/tex]
Fall time [tex]T_f= 3.70 seconds[/tex]
Generally the tension the bucket is mathematically given by
[tex]T-mg=ma[/tex]
For cylinder
[tex]T=I*\alpha[/tex]
where
[tex]I=1/2mR^2[/tex]
[tex]a=R*\alpha[/tex]
Giving
[tex]T=-1/2mR\alpha[/tex]
Therefore
[tex]a=\frac{-mg}{m+1/2m}[/tex]
[tex]a=\frac{-(1.9*9.81)}{1.9+0.5*(2.9)}[/tex]
[tex]a=-5.563880597 \approx -5.6m/s^2[/tex]
Generally the Newton's equation for motion is mathematically represented as
[tex]s=ut+1/2at^2[/tex]
[tex]s=0(3)+1/2*-5.6*(3.7)^2[/tex]
[tex]s=-38.332m[/tex]
