# Relativistic addition of velocities problem

**1. The problem statement, all variables and given/known data**

You are driving down a two-lane highway and a truck in the opposite lane travels toward you. Suppose the speed of light in a vacuum is 65 m/s. Determine the speed of the truck relative to you when

a – your speed is 25 m/s and the truck’s speed is 35 m/s and

b – your speed is 5 m/s and the truck’s speed is 55 m/s

The speeds given are relative to the ground

**2. Relevant equations**

V(ab) = Vac + Vcb / 1 + (Vac*Vcb/c^2)

**3. The attempt at a solution**

The velocity of the car (me) relative to the ground is Vac or 25 or 0.25c

Velocity of truck in opposite direction is Vcb or -35 or -0.35c

Plugging in to relativistic addition of velocities:

0.25c – 0.35c / 1 – (0.0.875)= -0.12c

Given that c = 65 for this problem, Vab = (-0.12)(65) = -7.1 m/s

I’m pretty sure that answer is wrong, because it makes no sense that the truck would be traveling at 7m/s relative to the car but I cannot figure out what I’m doing wrong here.

And for part B, I’m a little unclear on how "close" to the speed of light the velocities have to be in order to use the relativistic equation. Is 5 m/s far enough from the given speed of light (65 m/s) that I should use the "original recipe" addition of velocities to find the velocity of the truck? How would I know this?

Any help is greatly appreciated!

http://ift.tt/1lwi1Dy

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