1) The mass of the continent is ![3.3\cdot 10^{21} kg](https://tex.z-dn.net/?f=3.3%5Ccdot%2010%5E%7B21%7D%20kg)
2) The kinetic energy of the continent is 624 J
3) The speed of the jogger must be 4 m/s
Explanation:
1)
We start by finding the volume of the continent. We have:
is the side
is the depth
So the volume is
![V=L^2 t = (5.85\cdot 10^6)^2 (3.5\cdot 10^4)=1.20\cdot 10^{18} m^3](https://tex.z-dn.net/?f=V%3DL%5E2%20t%20%3D%20%285.85%5Ccdot%2010%5E6%29%5E2%20%283.5%5Ccdot%2010%5E4%29%3D1.20%5Ccdot%2010%5E%7B18%7D%20m%5E3)
We also know that its density is
![d=2750 kg/m^3](https://tex.z-dn.net/?f=d%3D2750%20kg%2Fm%5E3)
Therefore, we can find the mass by multiplying volume by density:
![m=dV=(2750)(1.20\cdot 10^{18})=3.3\cdot 10^{21} kg](https://tex.z-dn.net/?f=m%3DdV%3D%282750%29%281.20%5Ccdot%2010%5E%7B18%7D%29%3D3.3%5Ccdot%2010%5E%7B21%7D%20kg)
2)
The kinetic energy of the continent is given by:
![K=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where
is its mass
v = 3.2 cm/year is the speed
We have to convert the speed into m/s. We have:
3.2 cm = 0.032 m
![1 year = 1(365)(24)(60)(60)=3.15\cdot 10^7 s](https://tex.z-dn.net/?f=1%20year%20%3D%201%28365%29%2824%29%2860%29%2860%29%3D3.15%5Ccdot%2010%5E7%20s)
So, the speed is:
![v=\frac{0.032 m}{3.15 \cdot 10^7 s}=1.02\cdot 10^{-9} m/s](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B0.032%20m%7D%7B3.15%20%5Ccdot%2010%5E7%20s%7D%3D1.02%5Ccdot%2010%5E%7B-9%7D%20m%2Fs)
So, we can now find the kinetic energy:
![K=\frac{1}{2}(1.20\cdot 10^{21})(1.02\cdot 10^{-9})^2=624 J](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7D%281.20%5Ccdot%2010%5E%7B21%7D%29%281.02%5Ccdot%2010%5E%7B-9%7D%29%5E2%3D624%20J)
3)
Here we have a jogger of mass
m = 78 kg
And the jogger has the same kinetic energy of the continent, so
K = 624 J
The kinetic energy of the jogger is given by
![K=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where v is the speed of the jogger.
Solving for v, we find the speed that the jogger must have:
![v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(624)}{78}}=4 m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B2K%7D%7Bm%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%28624%29%7D%7B78%7D%7D%3D4%20m%2Fs)
Learn more about kinetic energy:
brainly.com/question/6536722
#LearnwithBrainly