(a) [tex]4.31\cdot 10^{14} J[/tex]
The energy lost by the meteorite is equal to its initial kinetic energy, since the meteorite comes to a stop, therefore it loses all its energy:
[tex]E_{lost}=K=\frac{1}{2}mv^2[/tex]
where
[tex]m=4.4\cdot 10^6 kg[/tex] is the mass of the meteorite
[tex]v=14 km/s = 14000 m/s[/tex] is the meteorite's speed
Substituting into the formula, we find
[tex]K=\frac{1}{2}(4.4\cdot 10^6 kg)(14000 m/s)^2=4.31\cdot 10^{14} J[/tex]
(b) 0.1 Megaton
1 Megaton (MT) corresponds to:
[tex]1 MT = 4.2\cdot 10^{15}J[/tex]
So, we can find how many MT the energy of the meteorite corresponds to by using the following proportion:
[tex]1 MT: 4.2 \cdot 10^{15} J = x : 4.31\cdot 10^{14} J[/tex]
Solving for x we find:
[tex]x=\frac{1 MT \cdot 4.31\cdot 10^{14}J}{4.2\cdot 10^{15} J}=0.1 MT[/tex]
(c) 7.9 Hiroshima bombs
1 kiloton (kT) corresponds to 1/1000 of megaton, so:
[tex]1 kT=\frac{4.2\cdot 10^{15}J}{1000}=4.2\cdot 10^{12} J[/tex]
As before, we can find how many kiloton the energy of the meteorite corresponds to by using the following proportion:
[tex]1 kT: 4.2 \cdot 10^{12} J = x : 4.31\cdot 10^{14} J[/tex]
Solving for x we find:
[tex]x=\frac{1 kT \cdot 4.31\cdot 10^{14}J}{4.2\cdot 10^{12} J}=103 kT[/tex]
The energy of the Hiroshima bomb was 13 kiloton, so the impact of the meteorite corresponds to:
[tex]n=\frac{103 kT}{13 kT}=7.9[/tex]
so, to 7.9 Hiroshima bombs.