Average Velocity for Three People's Trips

[Balsam]

Person A travels 10.2m/s[forward]. Person B travels 10.4m/s[forward]. Person C travels 3.51m/s[forward]. Find the average velocity for the trio.I added all 3 velocities(just the magnitudes) and divided by 3, but my answer was different from the textbook's. I got 8.0m/s[forward], but the answer in the book is 4.89m/s[forward]. I don't know what I did wrong.

 

[berkeman]

Person A travels 10.2m/s[forward]. Person B travels 10.4m/s[forward]. Person C travels 3.51m/s[forward]. Find the average velocity for the trio.I added all 3 velocities(just the magnitudes) and divided by 3, but my answer was different from the textbook's. I got 8.0m/s[forward], but the answer in the book is 4.89m/s[forward]. I don't know what I did wrong.

Please remember to use the Homework Help Template when posting here in the schoolwork forums. Thank you.

Now, please show your detailed calculations so we can look for any errors.

 

[Balsam]

Please remember to use the Homework Help Template when posting here in the schoolwork forums. Thank you.

Now, please show your detailed calculations so we can look for any errors.

10.2+10.4+3.51=24.11--> 24.11/3= ~8.0m. <-- That is what I did

 

[berkeman]

10.2+10.4+3.51=24.11--> 24.11/3= ~8.0m. <-- That is what I did

Your work looks correct. Are you sure you copied the problem statement correctly? Are you sure they all were moving in the same direction (forward)? Are they all facing the same direction as they move?

 

[Balsam]

Your work looks correct. Are you sure you copied the problem statement correctly? Are you sure they all were moving in the same direction (forward)? Are they all facing the same direction as they move?

Yes, I'm sure. All of the individual velocity values are given in the textbook, I copied them correctly.

 

[berkeman]

Yes, I'm sure. All of the individual velocity values are given in the textbook, I copied them correctly.

Is there a figure that goes with the question? Can you upload a picture of the question?

 

[NascentOxygen]

Person A travels 10.2m/s[forward]. Person B travels 10.4m/s[forward]. Person C travels 3.51m/s[forward]. Find the average velocity for the trio.

Are these traveling for identical times OR for identical distances?

Example: 3 friends in a car take turns at driving ...

EDIT: either way, still can't get the book's answer though

 

[256bits]

Are these traveling for identical times, or over identical distances?

Example: 3 friends in a car take turns at driving ...

EDIT: either way, still can't get the book's answer though

Try root mean square. Ans comes close.
That could be the method.

 

[Balsam]

Are these traveling for identical times OR for identical distances?

Example: 3 friends in a car take turns at driving ...

EDIT: either way, still can't get the book's answer though

I figured it out-- you have to add all of their displacements to get the total displacement, then add all of their times to get the total time, and then divide those 2 numbers to get their average velocity.

 

[NascentOxygen]

I figured it out-- you have to add all of their displacements to get the total displacement, then add all of their times to get the total time, and then divide those 2 numbers to get their average velocity.

Does that get you to the book's answer?

 

[NascentOxygen]

Try root mean square. Ans comes close.
That could be the method.

Interesting...but on what basis could you justify RMS?

 

[Balsam]

Does that get you to the book's answer?

Yeah, it does.

 

[NascentOxygen]

Yeah, it does.

Using your method I don't get the textbook's answer.

 

[256bits]

Interesting...but on what basis could you justify RMS?

RMS doesn't give the book answer either I believe, but I was considering a velocity distribution ( 3 points ?? ).
Is that valid for velocities in one direction - I can's say.
The answer seems to be weighted towards the slower individual though.