How Fast is the Other Car Going Relative to You?

[Hannah1]

Homework Statement

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?

Homework Equations

Your Car's Speed: 78 mph -->
Another Car's Speed: <-- 58 mph

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??

 

[CAF123]

Homework Statement

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?

Homework Equations

Your Car's Speed: 78 mph -->
Another Car's Speed: <-- 58 mph

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??

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)

 

[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 traveling 78mph relative to the ground, relative to yourself, the ground is traveling -78 mph relative to you (towards the negative y-axis). The other car is also traveling 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.

 

[CAF123]

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 traveling 78mph relative to the ground, relative to yourself, the ground is traveling -78 mph relative to you (towards the negative y-axis). The other car is also traveling 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.

Yes, and this can be verified by Galilean addition.

 

[Hannah1]

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 traveling 78mph relative to the ground, relative to yourself, the ground is traveling -78 mph relative to you (towards the negative y-axis). The other car is also traveling 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.

Yes, and this can be verified by Galilean addition.

So, according to Galilean addition, the answer would be:

-78 + -58 = -136

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

 

[Hannah1]

Help me?

 

[Hannah1]

What am I doing wrong? Please help.

 

[CAF123]

What am I doing wrong? Please help.

You are correct.