Answer:
A. topsoil the answer
Explanation:
I think its a correct answer
Answer:
a
![l_o =52 \ m](https://tex.z-dn.net/?f=l_o%20%20%3D52%20%5C%20%20m)
b
![l = 37.13 \ LY](https://tex.z-dn.net/?f=l%20%3D%2037.13%20%5C%20LY)
Explanation:
From the question we are told that
The speed of the spaceship is ![v = 0.800c](https://tex.z-dn.net/?f=v%20%20%3D%20%200.800c)
Here c is the speed of light with value ![c = 3.0*10^{8} \ m/s](https://tex.z-dn.net/?f=c%20%3D%20%203.0%2A10%5E%7B8%7D%20%5C%20m%2Fs)
The length is ![l = 31.2 \ m](https://tex.z-dn.net/?f=l%20%3D%2031.2%20%5C%20%20m)
The distance of the star for earth is ![d = 145 \ light \ years](https://tex.z-dn.net/?f=d%20%3D%20145%20%5C%20%20light%20%5C%20%20years)
The speed is ![v_s = 2.90 *10^{8}](https://tex.z-dn.net/?f=v_s%20%3D%202.90%20%2A10%5E%7B8%7D)
Generally the from the length contraction equation we have that
![l = l_o \sqrt{1 -[\frac{v}{c } ]}](https://tex.z-dn.net/?f=l%20%20%3D%20%20l_o%20%20%5Csqrt%7B1%20-%5B%5Cfrac%7Bv%7D%7Bc%20%7D%20%5D%7D)
Now the when at rest the length is ![l_o](https://tex.z-dn.net/?f=l_o)
So
![l_o =\frac{l}{\sqrt{ 1 - \frac{v^2}{c^2 } } }](https://tex.z-dn.net/?f=l_o%20%3D%5Cfrac%7Bl%7D%7B%5Csqrt%7B%201%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%20%7D%20%7D%20%7D)
![l_o =\frac{ 31.2 }{ \sqrt{1 - \frac{(0.800c ) ^2}{c^2} } }](https://tex.z-dn.net/?f=l_o%20%3D%5Cfrac%7B%2031.2%20%7D%7B%20%5Csqrt%7B1%20-%20%5Cfrac%7B%280.800c%20%29%20%5E2%7D%7Bc%5E2%7D%20%7D%20%7D)
![l_o=52 \ m](https://tex.z-dn.net/?f=l_o%3D52%20%5C%20%20m)
Considering b
Applying above equation
![l =l_o \sqrt{1 - [\frac{v}{c } ]}](https://tex.z-dn.net/?f=l%20%20%3Dl_o%20%5Csqrt%7B1%20-%20%20%5B%5Cfrac%7Bv%7D%7Bc%20%7D%20%5D%7D)
Here ![l_o =145 \ LY(light \ years )](https://tex.z-dn.net/?f=l_o%20%20%3D145%20%5C%20%20LY%28light%20%5C%20years%20%29)
So
![l=145 * \sqrt{1 - \frac{v_s^2}{c^2 } }](https://tex.z-dn.net/?f=l%3D145%20%2A%20%20%5Csqrt%7B1%20-%20%20%5Cfrac%7Bv_s%5E2%7D%7Bc%5E2%20%7D%20%7D)
![l =145 * \sqrt{ 1 - \frac{2.9 *10^{8}}{3.0*10^{8}} }](https://tex.z-dn.net/?f=l%20%3D145%20%2A%20%20%5Csqrt%7B%201%20-%20%5Cfrac%7B2.9%20%2A10%5E%7B8%7D%7D%7B3.0%2A10%5E%7B8%7D%7D%20%7D)
![l = 37.13 \ LY](https://tex.z-dn.net/?f=l%20%3D%2037.13%20%5C%20LY)
The gravitational force is gravity meanwhile the electric force is electric