Step-by-step explanation:
Formula that relates the mass of an object at rest and its mass when it is moving at a speed v:
![m=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bm_o%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%7D)
Where :
m = mass of the oebjct in motion
= mass of the object when at rest
v = velocity of a moving object
c = speed of the light = ![3\times 0^8 m/s](https://tex.z-dn.net/?f=3%5Ctimes%200%5E8%20m%2Fs)
We have :
1) Mass of the Dave = ![m_o=66 kg](https://tex.z-dn.net/?f=m_o%3D66%20kg)
Velocity of Dave ,v= 90% of speed of light = 0.90c
Mass of the Dave when moving at 90% of the speed of light:
![m=\frac{66 kg}{\sqrt{1-\frac{(0.90c)^2}{c^2}}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B66%20kg%7D%7B%5Csqrt%7B1-%5Cfrac%7B%280.90c%29%5E2%7D%7Bc%5E2%7D%7D%7D)
m = 151.41 kg
Mass of Dave when when moving at 90% of the speed of light is 151.41 kg.
2) Velocity of Dave ,v= 99% of speed of light = 0.99c
Mass of the Dave when moving at 99% of the speed of light:
![m=\frac{66 kg}{\sqrt{1-\frac{(0.99c)^2}{c^2}}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B66%20kg%7D%7B%5Csqrt%7B1-%5Cfrac%7B%280.99c%29%5E2%7D%7Bc%5E2%7D%7D%7D)
m = 467.86 kg
Mass of Dave when when moving at 99% of the speed of light is 467.86 kg.
3) Velocity of Dave ,v= 99.9% of speed of light = 0.999c
Mass of the Dave when moving at 99.9% of the speed of light:
![m=\frac{66 kg}{\sqrt{1-\frac{(0.999c)^2}{c^2}}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B66%20kg%7D%7B%5Csqrt%7B1-%5Cfrac%7B%280.999c%29%5E2%7D%7Bc%5E2%7D%7D%7D)
m = 1,467.17 kg
Mass of Dave when when moving at 99.9% of the speed of light is 1,467.17 kg.
4) Mass of the Dave = ![m_o=66 kg](https://tex.z-dn.net/?f=m_o%3D66%20kg)
Velocity of Dave,v=?
Mass of the Dave when moving at v speed of light: 500
![500 kg=\frac{66 kg}{\sqrt{1-\frac{(v)^2}{(3\times 10^8 m/s)^2}}}](https://tex.z-dn.net/?f=500%20kg%3D%5Cfrac%7B66%20kg%7D%7B%5Csqrt%7B1-%5Cfrac%7B%28v%29%5E2%7D%7B%283%5Ctimes%2010%5E8%20m%2Fs%29%5E2%7D%7D%7D)
![v=2.973\times 10^8 m/s](https://tex.z-dn.net/?f=v%3D2.973%5Ctimes%2010%5E8%20m%2Fs)
Dave should be moving at speed of
.