# Q & A: Jumping between cars

Q:
If you are on top of a car traveling 30 mph and there is a vehicle traveling the same speed in front, if you jump from the car behind to the vehicle in front, will you be traveling more than 30 mph in the short distance from the car behind and the vehicle in front?
- andrew , 24
ireland
A:
This is a problem in relativity.  The speed depends on what frame of reference you measure it in.  Suppose the jumper travels at a speed of 5 mph relative to the car.   According to his friend who is riding along with him, his speed is 5 mph.   According to another friend who is observing from the ground it is Vcar + Vjump = 30 + 5 = 35.   There are corrections due to special relativity but they are small potatoes in this case.  The correct relativistic expression for the addition of velocities is:
Vsum = ( Vcar + Vjump )/( 1 + Vcar Vjump / c2 ).

Now since both Vcar  and  Vjump are tiny compared to c, the velocity of light, the relativistic correction is completely negligible.

LeeH

(published on 03/29/2010)