1) Mass of the continent: [tex]2.2\cdot 10^{21} kg[/tex]
2) Kinetic energy: 1118 J
3) Speed of the jogger: 5.3 m/s
Explanation:
1)
First of all, we calculate the volume of the continent. It is a slab of side
[tex]L=5100 km = 5.1\cdot 10^6 m[/tex]
and thickness
[tex]t=30 km = 3.0\cdot 10^4 m[/tex]
So its volume is
[tex]V=tL^2=(3.0\cdot 10^4)(5.1\cdot 10^6)^2=7.8\cdot 10^{17} m^3[/tex]
The density of the slab is
[tex]\rho = 2850 kg/m^3[/tex]
Therefore, we can calculate the mass using the relationship
[tex]\rho = \frac{m}{V}[/tex]
where m is the mass. And solving for m,
[tex]m=\rho V=(2850)(7.8\cdot 10^{17})=2.2\cdot 10^{21} kg[/tex]
2)
The kinetic energy of the continent is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
[tex]m=2.2\cdot 10^{21} kg[/tex] is its mass
v = 3.8 cm/year is its speed
We have to convert the speed into m/s. Keeping in mind that
1 cm = 0.01 m
[tex]1 year = 365\cdot 24\cdot 60 \cdot 60 =3.15\cdot 10^7 s[/tex]
We find
[tex]v=3.18 \frac{cm}{y} \cdot \frac{0.01}{365\cdot 24 \cdot 60 \cdot 60}=1.0\cdot 10^{-9} m/s[/tex]
So now we can find the kinetic energy:
[tex]K=\frac{1}{2}(2.2\cdot 10^{21})(1.0\cdot 10^{-9})^2=1118 J[/tex]
3)
The kinetic energy of the jogger is given by
[tex]K=\frac{1}{2}m'v'^2[/tex]
where
m' = 80 kg is the mass of the jogger
v' is the speed of the jogger
Here we want the jogger to have the same kinetic energy of the continent, so
[tex]K=1118 J[/tex]
And by re-arranging the equation, we can find what speed the jogger must have:
[tex]v'=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(1118)}{80}}=5.3 m/s[/tex]
Learn more about kinetic energy:
brainly.com/question/6536722
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