A) The mass of the continent is [tex]2.5\cdot 10^{21} kg[/tex]
B) The kinetic energy is 2016 J
C) The speed of the jogger should be 7.1 m/s
Explanation:
A)
The mass of the continent can be calculated as
[tex]m = \rho V[/tex]
where
[tex]\rho = 2800 kg/m^3[/tex] is its density
V is its volume
We have to calculate its volume. We know that the continent is represented as a slab of side 5900 km (so its surface is 5900 x 5900, assuming it is a square) and depth of 26 km, so its volume is:
[tex]V=(5900 km)^2 (26 km)=9.05\cdot 10^8 km^3 =9.05 \cdot 10^8 \cdot (10^9 m^3/k^3)=9.05\cdot 10^7 m^3[/tex]
So, the mass of the continent is
[tex]m=\rho V = (2800)(9.05\cdot 10^{17})=2.5\cdot 10^{21} kg[/tex]
B)
The kinetic energy of a body is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the body
v is its speed
For the continent, we have:
[tex]m=2.5\cdot 10^{21} kg[/tex] is the mass
[tex]v=4 cm/year[/tex] is the speed
We have to convert the speed into SI units. we have:
1 cm = 0.01 m
[tex]1 year = (365)(24)(60)(60) s = 3.15\cdot 10^7 s[/tex]
So, the speed is
[tex]v=4 cm/year = 0.04 m/year \cdot \frac{1}{3.15\cdot 10^7}=1.27\cdot 10^{-9} m/s[/tex]
Therefore, the kinetic energy is
[tex]K=\frac{1}{2}(2.5\cdot 10^{21} kg)(1.27\cdot 10^{-9} m/s)^2=2016 J[/tex]
C)
Again, the kinetic energy of an object is
[tex]K=\frac{1}{2}mv^2[/tex]
For the jogger in this problem, his mass is
m = 80 kg
And we want its kinetic energy to be equal to that of the continent, so
K = 2016 J
Re-arranging the equation for v, we find what speed the jogger needs to have this kinetic energy:
[tex]v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(2016)}{80}}=7.1 m/s[/tex]
Learn more about kinetic energy here:
brainly.com/question/6536722
#LearnwithBrainly
