Answers:
a) [tex]2.82(10)^{21} kg[/tex]
b) [tex]1410 J[/tex]
c) [tex]36.62 m/s[/tex]
Explanation:
Density [tex]\rho[/tex] is defined as a relation between mass [tex]m[/tex] and volume [tex]V[/tex]:
[tex]\rho=\frac{m}{V}[/tex] (1)
Where:
[tex]\rho=2720 kg/m^{3}[/tex] is the average density of the continent
[tex]m[/tex] is the mass of the continent
[tex]V[/tex] is the volume of the continent, which can be estimated is we assume it as a a slab of rock 5300 km on a side and 37 km deep:
[tex]V=(length)(width)(depth)=(5300 km)(5300 km)(37 km)=1,030,330,000 km^{3} \frac{(1000 m)^{3}}{1 km^{3}}=1.03933(10)^{18} m^{3}[/tex]
Finding the mass:
[tex]m=\rho V[/tex] (2)
[tex]m=(2720 kg/m^{3})(1.03933(10)^{18} m^{3})[/tex] (3)
[tex]m=2.82(10)^{21} kg[/tex] (4) This is the mass of the continent
Kinetic energy [tex]K[/tex] is given by the following equation:
[tex]K=\frac{1}{2}mv^{2}[/tex] (5)
Where:
[tex]m=2.82(10)^{21} kg[/tex] is the mass of the continent
[tex]v=4.8 \frac{cm}{year} \frac{1 m}{100 cm} \frac{1 year}{365 days} \frac{1 day}{24 hours} \frac{1 hour}{3600 s}=1(10)^{-9} m/s[/tex] is the velocity of the continent
[tex]K=\frac{1}{2}(2.82(10)^{21} kg)(1(10)^{-9} m/s)^{2}[/tex] (6)
[tex]K=1410 J[/tex] (7) This is the kinetic energy of the continent
If we have a jogger with mass [tex]m=77 kg[/tex] and the same kinetic energy as that of the continent [tex]1413 J[/tex], we can find its velocity by isolating [tex]v[/tex] from (5):
[tex]v=\sqrt{\frac{2 K}{m}}[/tex] (6)
[tex]v=\sqrt{\frac{2 (1413 J)}{77 kg}}[/tex]
Finally:
[tex]v=36.62 m/s[/tex] This is the speed of the jogger
