Calculating Displacement in Relative Motion

[Balsam]

Homework Statement

A person on a bus walks to the front of the bus at 3.0 km/h relative to the bus, while the bus travels south at 15km/h. What is the passenger's total displacement?

Homework Equations

displacement= final position-initial position
total displacement=displacement1+displacement2

The Attempt at a Solution

Do you draw vectors to do this? I have no clue what to do.

 

[CWatters]

Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).

 

[Balsam]

Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).

The question

Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).

The question asks for the passesnger's velocity relative to the road, but I was unsure about how to find displacement because you need displacement to calculate velocity.

 

[SteamKing]

The question

The question asks for the passesnger's velocity relative to the road, but I was unsure about how to find displacement because you need displacement to calculate velocity.

No, you don't. Velocity is a vector quantity. Vector quantities can be added and subtracted vectorially.

 

[Balsam]

No, you don't. Velocity is a vector quantity. Vector quantities can be added and subtracted vectorially.

So how would you calculate the velocity, because the question only gives you 2 speed values?

 

[SteamKing]

So how would you calculate the velocity, because the question only gives you 2 speed values?

Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.

 

[Balsam]

Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.

I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.

 

[SteamKing]

I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.

Displacement is a change in position. It is a vector.
Distance is a change in position. It is a scalar.

http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

Nothing is said in the problem about the bus going backwards and forwards. As far as you know, the bus is traveling south at 15 km/hr till the end of time. The guy in the aisle is walking forward at 3 km/hr relative to the bus. If you were standing on the side of the road as this bus and passenger passed you, what would be the speed of the passenger relative to you?

 

[Ray Vickson]

Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.

I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.

What you are saying is true. (Average) speed = sum of the absolute values of displacement, divided by the total trip time. The summation is over the separate "legs" of the journey. In your example, the speed on the forward portion is 2 m/s, so the displacement is 2t (m) (where t = forward trip time in seconds). The displacement on the backward portion is 2t as well; t must be the same because the distances and speeds are the same on both legs of the trip. So, the total absolute displacement = 2t + 2t = 4t, while the total trip time = 2t; thus, speed = 4t/2t = 2 (m/s). And, of course, velocity = 0, just as you said.

 

[CWatters]

Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.

Some examples of velocity...

100mph heading North.

60 meters per second vertically upwards.

4kts heading west along the equator.

 

[Balsam]

Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.

Some examples of velocity...

100mph heading North.

60 meters per second vertically upwards.

4kts heading west along the equator.

So wouldn't the person's velocity just be 3km/h[N]? If so, what was the point of the bus' speed being given?

 

[SteamKing]

So wouldn't the person's velocity just be 3km/h[N]? If so, what was the point of the bus' speed being given?

According to you, the problem asks for the passenger's velocity relative to the road. This is why Item No. 1 in the HW template asks posters to provide a complete problem statement.

Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.

Emphasis added.
Except, according to Post #3, the problem asks for the passenger's velocity relative to the road.

 

[CWatters]

Except, according to Post #3, the problem asks for the passenger's velocity relative to the road.

I agree. I think the OP was confused by..

Speed + Direction = Velocity.

eg It's not regular addition.