Relativity in X & Y Axis'-a, V, r

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In summary, Liza's velocity relative to Jill/from Jill's perspective is +10 m/s and their distance is 5.00 meters. Liza's acceleration relative to Jill/from Jill's perspective is -0.25 m/s2.
  • #1
Const@ntine
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Homework Statement



Liza is driving her Lamborghini with an acceleration of a=(3.00i - 2.00j) m/s^2, while Jill is driving her Jaguar with an acceleration of (1.00i + 3.00j) m/s^2. Both begin from a state of rest, beginning at the start of the XY axis'. After 5.00s:

a) What's the magnitude of the Liza's Velocity relative to Jill/from Jill's perspective?
b) What's their distance?
c) What's Liza's acceleration relative to Jill/from Jill's perspective?

Homework Equations



X: Vf = Vi + a*t || Xf = Xi +Vi*t + 1/2*a*t^2

Y: Vf = Vi + a*t || Yf = Yi +Vi*t + 1/2*a*t^2

The Attempt at a Solution



I did all the necessary actions to find the Velocities and all that, but I took each Axis differently, found the relative quantities in each axis, and then I did the Pythagorean Theorem to find the combined one.

a)

Liza: X: Vf = 3m/s^2 * 5s = +15 m/s^2 || Y: Vf = ... = -10 m/s^2

Jill: X: Vf = ... = +5 m/s^2 || Y: Vf = ... = +15 m/s^2

Now, the problem is that I haven't really grasped how relativity works when I'm dealing with two Axis'. My book has only two examples, which are fairly basic, and don't really help me with such problems. The first one is the classic "man on sliding treadmill", with one woman on the ground and another on the treadmil. The other example is the boat and the river's stream.

So, I don't really have anything to look at that'll help me understand how this really works, as the pages devoted to it are just about two. So, I tackled it a bit with logic, and tried to match the numbers in order to get the correct results from the book, but I'd really appreciate some help in understanding why this happens, and how I'll use it in other problems.

Anyway, back to the question, I followed with this:

X: Vlj = Vlo - Vjo = (15 - 5) m/s = +10 m/s

Y: Vlj = Vlo - Vjo = (-10 -15) m/s = -25 m/s

I thought about it like this: Say I'm in Jill's car (the j) and Liza's in front of us (the l). Liza's velocity relative to mine's should be: Her initial velocity, relative to the starting point/Earth (the o), minus my velocity relative to the starting point/earth.

And I went ahead and did the same with the other quantities. I found the correct results, but I just want to see if I'm tackling this the right way, or I just happened too find the same results, but with a flawed way of thinking.
 
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  • #2
Now, the problem is that I haven't really grasped how relativity works when I'm dealing with two Axis'.
... works the same way as one axis, only you are doing a vector subtraction.

ie. If ##\vec v_x|_y## is the velocity of X wrt Y, while ##v_x## and ##v_y## are the velocities of X and Y wrt a common reference frame (ie the ground), then
##\vec v_x|_y = \vec v_x-\vec v_y## You can see this is right because ##\vec v_y|_y=0## ... that is to say that Y is stationary wrt itself.

I thought about it like this: Say I'm in Jill's car (the j) and Liza's in front of us (the l). Liza's velocity relative to mine's should be: Her initial velocity, relative to the starting point/Earth (the o), minus my velocity relative to the starting point/earth.
Looks good to me. Check - if Jill was going faster that Lisa, then Liza would be going backwards wrt to Jill. Or - your own velocity with repect to yourself would be zero.
 
  • #3
Simon Bridge said:
... works the same way as one axis, only you are doing a vector subtraction.

ie. If ##\vec v_x|_y## is the velocity of X wrt Y, while ##v_x## and ##v_y## are the velocities of X and Y wrt a common reference frame (ie the ground), then
##\vec v_x|_y = \vec v_x-\vec v_y## You can see this is right because ##\vec v_y|_y=0## ... that is to say that Y is stationary wrt itself.

Looks good to me. Check - if Jill was going faster that Lisa, then Liza would be going backwards wrt to Jill. Or - your own velocity with repect to yourself would be zero.

Thanks for the tip!
 

What is relativity in the X and Y axis?

Relativity in the X and Y axis refers to the concept of how objects in motion are affected by their position and velocity in relation to other objects in a two-dimensional space. This is commonly described by the equations for acceleration (a), velocity (V), and position (r).

How does relativity in the X and Y axis differ from relativity in the Z axis?

Relativity in the X and Y axis is specific to motion in a two-dimensional space, while relativity in the Z axis involves motion in a three-dimensional space. This means that the equations and principles used to describe relativity in the X and Y axis may differ from those used in the Z axis.

Why is relativity in the X and Y axis important in physics?

Relativity in the X and Y axis is important in physics because it helps us understand how objects move and interact in a two-dimensional space. This is crucial in many real-world applications, such as navigation, robotics, and satellite technology.

Can relativity in the X and Y axis be applied to everyday situations?

Yes, relativity in the X and Y axis can be applied to everyday situations. For example, when you are driving a car, your position and velocity in relation to other objects on the road are constantly changing, and this can be described using the principles of relativity in the X and Y axis.

How does relativity in the X and Y axis relate to Einstein's theory of general relativity?

While Einstein's theory of general relativity is a more complex and comprehensive theory, it is based on the principles of relativity in the X and Y axis. The equations for acceleration, velocity, and position in the X and Y axis are the building blocks for understanding the effects of gravity and the curvature of spacetime in general relativity.

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