<h2>
Answers:</h2>
The expression for the relativistic energy
is given by:
(1)
being ![c=3(10)^{8}m/s](https://tex.z-dn.net/?f=c%3D3%2810%29%5E%7B8%7Dm%2Fs)
This famous equation includes the relativistic Kinetic energy
and the energy at rest
:
(2)
Where:
(3)
Being
the mass at rest for the meteorite
(4)
In addition, there is a relation between the relativistic energy and the momentum
:
(5)
Where:
(6)
Knowing this, let's begin with the answers:
<h2>
a)Momentum</h2>
In order to solve this part, equation (6) will be helpful, since we already know the mass of the meteorite and its speed
:
![p=\frac{m_{o}v}{\sqrt{1-\frac{v^{2}}{c^{2}}}}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Bm_%7Bo%7Dv%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D)
![p=\frac{(1500kg)(0.7c)}{\sqrt{1-\frac{(0.7c)^{2}}{c^{2}}}}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B%281500kg%29%280.7c%29%7D%7B%5Csqrt%7B1-%5Cfrac%7B%280.7c%29%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D)
![p=\frac{(1500kg)(0.7(3(10)^{8}m/s))}{\sqrt{1-0.49}}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B%281500kg%29%280.7%283%2810%29%5E%7B8%7Dm%2Fs%29%29%7D%7B%5Csqrt%7B1-0.49%7D%7D)
(7) >>>>This is the meteorite's momentum
<h2>
b) Total Energy</h2>
Remembering equation (5), which relates the total energy with the momentum:
![E=\sqrt{p^{2}c^{2}+m_{o}^{2}c^{4}}](https://tex.z-dn.net/?f=E%3D%5Csqrt%7Bp%5E%7B2%7Dc%5E%7B2%7D%2Bm_%7Bo%7D%5E%7B2%7Dc%5E%7B4%7D%7D)
We can substitute the value of the momentum found on (7):
![E=\sqrt{(4.411(10)^{11}kg.m/s)^{2}(3(10)^{8}m/s)^{2}+(1500kg)^{2}(3(10)^{8}m/s)^{4}}](https://tex.z-dn.net/?f=E%3D%5Csqrt%7B%284.411%2810%29%5E%7B11%7Dkg.m%2Fs%29%5E%7B2%7D%283%2810%29%5E%7B8%7Dm%2Fs%29%5E%7B2%7D%2B%281500kg%29%5E%7B2%7D%283%2810%29%5E%7B8%7Dm%2Fs%29%5E%7B4%7D%7D)
Then:
![E=1.890(10)^{20}kg.m^{2}/s^{2}](https://tex.z-dn.net/?f=E%3D1.890%2810%29%5E%7B20%7Dkg.m%5E%7B2%7D%2Fs%5E%7B2%7D)
Knowing
:
(8)>>>This is the total energy of the meteorite
<h2>c) Energy at rest</h2>
Using equation (3):
(9) >>>Meteorite's energy at rest
<h2>d) Relativistic kinetic energy</h2>
According to equation (4) the relativistic kinetic energy depends on the total energy and the energy at rest:
We already know the values of
and
from (8) and (9). Hence we only have to substitute them on the equation:
>>>Meteorite's Relativistic energy