# Relative Speed of Two Cars

1. Oct 10, 2012

### Hannah1

1. The problem statement, all variables and given/known data
Your car is going 78 mph on the freeway. Another car is going 58 mph in the opposite direction. How fast is the person in the other car going, relative to you?

2. Relevant equations
Your Car's Speed: 78 mph -->
Another Car's Speed: <-- 58 mph

3. The attempt at a solution
(78 mph) -------->
<------ (58 mph)

78 - 58 = 20

Wouldn't the other car be going -20 mph relative to my car??

2. Oct 10, 2012

### CAF123

Let $\vec{v}_{CF}$ be the velocity of your car relative to the freeway.
Let $\vec{v}_{C'C}$ be the velocity of the other car relative to your car.
Let $\vec{v}_{C'F}$ be the velocity of the other car relative to the freeway.

Use Galilean velocity addition to find the correct velocity. (This should correct your sign error)

3. Oct 10, 2012

### PhizKid

I'm new at this myself but I think it's -78 + -58 because if you pretend you are sitting in your car, facing upwards (towards the positive y-axis), and you are at rest. Since you are travelling 78mph relative to the ground, relative to yourself, the ground is travelling -78 mph relative to you (towards the negative y-axis). The other car is also travelling in the same direction as the ground relative to you, so I think you have to add both speeds relative to you, which are both negative. I could be wrong, though.

4. Oct 10, 2012

### CAF123

Yes, and this can be verified by Galilean addition.

5. Oct 10, 2012

### Hannah1

-78 + -58 = -136

AKA, the person in the other car is going 136 mph relative to me. Correct??

6. Oct 10, 2012

### Hannah1

Help me?

7. Oct 11, 2012