Relative velocity problem

  • #1
Suppose two bodies A and B are moving perpendicular to each other with velocities 'a' and 'b'.

A with 'a'
^
|
|
|
|
|
|
|
|
|
---------------------------------------------->B with 'b'


Now how would they measure their relative velocitites?As A's velocity in the direction of motion of B = 0 ,B would feel that A is moving away(linearly) from it with a velocity'b'
And A would feel that B is moving away with velocity 'a'.

Now how do we compare their relative velocity? This is in order to aply the Lorentz transfomation.
 

Answers and Replies

  • #2
Meir Achuz
Science Advisor
Homework Helper
Gold Member
3,529
114
To find A's velocity with respect to B, make a LT with velocity b, using the transformation laws for velocity a (separate law for a perp and a parallel to b).
 
  • #3
932
0
Or rotate the system so that A and B are moving away from each other along an axis.
 
  • #4
But the velocities of A and B have components that hav the value of 0 in their respective axes.

Like if A measures velocity of B in his direction of motion,it comes out to be zero :(
Im confused
 
  • #5
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
Like if A measures velocity of B in his direction of motion,it comes out to be zero :(
No it doesn't. Remember that A is moving upwards in your diagram.
 
  • #6
Yea i get that,but in his DIRECTION of motion wouldnt he be measuring the velocity of B as zero?
 
  • #7
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
Okay, try it this way. How fast is B moving away from A from A's rest frame?
 
  • #8
with velocity 'a'? and with veolcity 'b' in the direction of the perpendicular axis
 
  • #9
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
with velocity 'a'? and with veolcity 'b' in the direction of the perpendicular axis
Yes, so what is the magnitude of this velocity?
 
  • #11
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
Perhaps, the hypotenuse of your triangle...
 
  • #12
ok ok sry its the resultant of the two vectors sry :p.How foolish of me
 
  • #13
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
ok ok sry its the resultant of the two vectors sry :p.How foolish of me
No problem, and the direction of the resultant vector is...?
 
  • #14
the positive direction of the x axis.BBut one more question..wudnt we do resultantcos(theta) to get the magnitude of the vector in the reference frame's exact direction?
 
  • #15
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
  • #16
y isnt it ??????

r(x)=a(x) +b(x)
r(y)=a(y) +b(y)

r=r(x)i + r(y)j

r(x)=b
r(y)=a

so y isnt it?the answer is positive
 
  • #17
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
Think about it for a minute. What is the direction of the resultant velocity (think about the 'poeple swimming across a river' questions that I'm sure you've done.)
 
  • #18
umm i havent done the above stated question.Im n grade 10.


but wats wrong with the resultant as i said in my previous post?
 
  • #19
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
I asked for the direction of the resultant velocity and you haven't given it, you've just given two components, which is what we were given at the start of the problem.
 
Last edited:
  • #20
r(x) is positive and so is r(y)

so
r=b i+a j

So whats the problem if theyre in the positive direction of the x and y axes?
 
  • #21
robphy
Science Advisor
Homework Helper
Insights Author
Gold Member
5,777
1,074
IMHO, in spite of the subject matter, this thread seems more like a homework-type question.
 
  • #22
Hehe,but i cant get y im wrong:S
 
  • #24
err..thnx
but still please tell me if both r(x) and r(y) are positive wats wrong?

sry but i still cant get it
 
  • #25
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
6
When I say resultant vector, what does that mean to you?
 

Related Threads on Relative velocity problem

Replies
6
Views
770
Top