Relative Motion problem involving a moving person and a moving bus

[rasofia77]

1. Problem Statement: What is the velocity of John relative the bus in each of the following situations:

A) John is sitting on the street and the bus is moving at 30m/s toward him
B)John is sitting in his car traveling North at 25m/s toward a stationary bus?
C)John is sitting in his car traveling North at 35 m/s and the bus is moving 15 m/s toward him?

2. Relevant Equations: oVe=oVm+mVe3. Work on the Solution: So I'm struggling a bit with relative motion, but these are my thought processess

A)Ok, so John is sitting and the bus is coming at him with a velocity of 30...Since it's asking for 'velocity of John relative the bus'...I see it in the bus's perspective, John would look like he's going toward it..therefore he would look like he's going 30 m/s south, which is -30 m/s (BUT, the answer, as my teacher let me know, is positive 30, so 30 north...why is that?)

B) Ok now, the bus, again sees John traveling to it at 25 m/s, so again I would think that would be South since to the bus it looks that way..so -25m/s...but the answer is positive, so north.
Actually, I used this equation: jVb=jVe + eVj ... 25-0=25 ...so I know why it's positive in terms of the equation, but I want to know how logically..

C)For this one, I think I just used the equation, so johnVearth=35 and busVearth=-15. Therefore johnVbus= johnVearth + earthVbus ---> jVb= (35)+(15) ...since eVb is opposite of bVe...so that's 50m/s. And that's the correct answer.

Basically, my real question here is..how does all this make sense logically..not numerically/factually...but how can I see it in a way that it makes sense- the directions and all. And for the first one especially, why North, not South? Shouldn't it be relative to the bus, the way the bus sees it?

 

[siddharth23]

In the first case, North or South is not mentioned. It's just mentioned that the bus is moving towards him. -30 would mean that the bus is going away from him.

In the second case, why would it appear to the bus that John is traveling South? Imagine yourself sitting in that stationary bus and John moving towards the North. That is exactly how you'll see it.

I know it all seems a bit complicated at first. You need some time to make sense of it all, I've been there. It could be made a bit easier by visualizing yourself in that position. The -ve and +ve are just used for opposite directions. It's not necessary that +ve is North and -ve is South. It's just a convention we use.

 

[rasofia77]

In the first case, North or South is not mentioned. It's just mentioned that the bus is moving towards him. -30 would mean that the bus is going away from him.

In the second case, why would it appear to the bus that John is traveling South? Imagine yourself sitting in that stationary bus and John moving towards the North. That is exactly how you'll see it.

I know it all seems a bit complicated at first. You need some time to make sense of it all, I've been there. It could be made a bit easier by visualizing yourself in that position. The -ve and +ve are just used for opposite directions. It's not necessary that +ve is North and -ve is South. It's just a convention we use.

I guess I was/am confused because (since it's velocity of John relative to the bus), I saw it as in...if John is going towards the bus, then in the bus's perspective, it looks like John is coming right at it, so it looks like John is going southward to it...I don't know, I'm all over the place with these problems...but I guess I sort of understand. If John is going North, John is going North...the perspective won't change the direction is what you're saying right?

 

[siddharth23]

Right!
Now relative to John, the bus is going South. But John is going North.

 

[rasofia77]

Right!
Now relative to John, the bus is going South. But John is going North.

Oh okay, thanks!

 

[PTx]

For "C)For this one, I think I just used the equation, so johnVearth=35 and busVearth=-15. Therefore johnVbus= johnVearth + earthVbus ---> jVb= (35) +(15)"
Shouldn't it be jvb= 35 -15? Because the bus (BvE) is moving 15 m/s South while John (JvE) is moving 35 m/s North
So JvB should =JvE - EvB -> JvB= 35 - 15 -> John's speed in view of the Bus to be 15 m/s?

 

[hmmm27]

(Note that this is an almost 7 year old thread, I'm guessing we won't get much input from the OP)

Hi, PTx ; if you look at the problem statement :

1. What is the velocity of John relative the bus in each of the following situations:
A) John is sitting on the street and the bus is moving at 30m/s toward him
B)John is sitting in his car traveling North at 25m/s toward a stationary bus?
C)John is sitting in his car traveling North at 35 m/s and the bus is moving 15 m/s toward him?

you may notice that there's no way of answering all three in the "stationary" framework. (you might be able to pull it off for 'B').

The bus (and John) are both points; the only direction component of the velocities that work for all 3 is "coming" and "going" (I can't remember which one is + and -). The answers to A and B are reasonably obviously 30m/s and 25m/s, both with the direction component "coming" or "approaching".

For "C)For this one, I think I just used the equation, so johnVearth=35 and busVearth=-15. Therefore johnVbus= johnVearth + earthVbus ---> jVb= (35) +(15)"
Shouldn't it be jvb= 35 -15? Because the bus (BvE) is moving 15 m/s South while John (JvE) is moving 35 m/s North
So JvB should =JvE - EvB -> JvB= 35 - 15 -> John's speed in view of the Bus to be 15 m/s?

C states that John is moving North, but doesn't give the bus's velocity in the external framework. How do you get "South" ?

 

[PTx]

(Note that this is an almost 7 year old thread, I'm guessing we won't get much input from the OP)

Hi, PTx ; if you look at the problem statement :

you may notice that there's no way of answering all three in the "stationary" framework. (you might be able to pull it off for 'B').

The bus (and John) are both points; the only direction component of the velocities that work for all 3 is "coming" and "going" (I can't remember which one is + and -). The answers to A and B are reasonably obviously 30m/s and 25m/s, both with the direction component "coming" or "approaching".C states that John is moving North, but doesn't give the bus's velocity in the external framework. How do you get "South" ?

I see my mistake, I got south thinking that since John is traveling north and the Bus is traveling towards him, I thought that the bus was traveling in the opposite direction towards him. Like the bus is above John, traveling South towards him while he is traveling North towards the bus above him.

But, Why is JvB 50 m/s?
Wait, is it because they are traveling in the same direction? If they are then it makes sense.