1) The mass of the continent is [tex]3.3\cdot 10^{21}kg[/tex]
2) The kinetic energy of the continent is 1683 J
3) The speed of the jogger must be 6.57 m/s
Explanation:
1)
The continent can be represented as a slab of size
[tex]d=5850 km = 5.85\cdot 10^6 m[/tex]
and depth
[tex]t = 35 km = 3.5\cdot 10^4 m[/tex]
So its volume is
[tex]V=d^2 t = (5.85\cdot 10^6)^2(3.5\cdot 10^4)=1.20\cdot 10^{18} m^3[/tex]
We also know that the density of the continent is
[tex]\rho = 2750 kg/m^3[/tex]
Therefore, we can calculate its mass as:
[tex]m=\rho V=(2750)(1.20\cdot 10^{18})=3.3\cdot 10^{21} kg[/tex]
2)
The kinetic energy of the continent is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is its mass
v is its speed
We have already calculate its mass, while the speed is
v = 3.2 cm/year
We have to convert into SI units first, as follows:
[tex]v=3.2 \frac{cm}{year} \cdot \frac{1}{100 cm/m} \cdot \frac{1}{(365 d/y)(24h/d)(60min/h)(60 s/min)}=1.01\cdot 10^{-9} m/s[/tex]
The mass is
[tex]m=3.3\cdot 10^{21} kg[/tex]
So, the kinetic energy of the continent is
[tex]K=\frac{1}{2}(3.3\cdot 10^{21})(1.01\cdot 10^{-9})^2=1683 J[/tex]
3)
Here we have a jogger having the same kinetic energy of the continent, so
[tex]K=1683 J[/tex]
And the kinetic energy of the jogger can be expressed as
[tex]K=\frac{1}{2}mv^2[/tex]
where
m = 78 kg is the mass of the jogger
v is his speed
We can therefore re-arrange the equation to find the speed of the man, and we get:
[tex]v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(1683)}{78}}=6.57 m/s[/tex]
Learn more about kinetic energy:
brainly.com/question/6536722
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