Answer:
6.04788 in
[tex]115.82654\ in^3[/tex]
78.38779 m/s
0.88159 kg
34.55294 J
Explanation:
Circumference is given by
[tex]c=2\pi r\\\Rightarrow r=\dfrac{c}{2\pi}\\\Rightarrow r=\dfrac{19}{2\pi}\\\Rightarrow r=3.02394\ in[/tex]
Diameter is given by
[tex]d=2r\\\Rightarrow d=2\times 3.02394\\\Rightarrow d=6.04788\ in[/tex]
The diameter is 6.04788 in
[tex]6.04788\times 2.54=15.3616152\ cm[/tex]
Volume of sphere is given by
[tex]v=\dfrac{4}{3}\pi r^3\\\Rightarrow v=\dfrac{4}{3}\pi 3.02394^3\\\Rightarrow v=115.82654\ in^3[/tex]
The volume is [tex]115.82654\ in^3[/tex]
[tex]115.82654\times \dfrac{1}{1728}=0.06702\ ft^3[/tex]
Fall velocity is given by
[tex]V=k\sqrt{d}\\\Rightarrow V=20\sqrt{15.3616152}\\\Rightarrow V=78.38779\ m/s[/tex]
The velocity of the fall will be 78.38779 m/s
Mass is given by
[tex]m=\rho v\\\Rightarrow m=29\times 0.06702\\\Rightarrow m=1.94358\ lb[/tex]
[tex]1.94358\ lb=1.94358\times \dfrac{1}{2.20462}=0.88159\ kg[/tex]
The mass is 0.88159 kg
Kinetic energy is given by
[tex]K=\dfrac{1}{2}mv^2\\\Rightarrow K=\dfrac{1}{2}0.88159\times 78.38779\\\Rightarrow K=34.55294\ J[/tex]
The kinetic energy is 34.55294 J