Railguns: a weapon that fires aluminum bullets close to the speed of light, but somehow take time to hit the target and can be dodged. When people are hit by these... strangely slow but fast at the same time bullets, they go flying backwards like they just got hit by a car. So lets take a look at the momentum of these bullets.
Formula: (Mb)(Vf)+ (Mp)(Vpf) = (Mb)(Vi)+(Mp)(Vpi)
But because the bullet and the person start at 0 m/s, we set the equation = 0 and solve for the person (p)'s final velocity. The average male in north america weighs 80.7 kg.
in this problem, Mb refers to refers to the mass of the bullet.
So the mass of the average bullet made of lead is 0.0042 kg. The bullet's initial velocity is 0 m/s and it's final velocity is .9*c which is 269,813,212.2 m/s. So the total formula is
(0.042kg)(269,813,212.2 m/s) + (80.7 kg)(? m/s) = 0
So then we get:
12,411,407.8 kg/m/s = -80.7(x)
then divide the momentum of the bullet by the mass of the person = -153,796.8 m/s
So just from the gun's recoil, the man would be flying backwards at over 150,000 m/s.
Now for how fast a person hit by a bullet flying at that speed would fly backwards.
So now the formula changes to:
(0.042kg)(?)+(80.7 kg)(?) = (0.042 kg)(269,813,213.2 m/s) + (80.7 kg)(0 m/s)
80.742(x) = 11,332,154.91
x = 140,350 m/s
So the person shot would fly in the forward direction at 140,350 m/s.
Gotta go fast.