Relativity Question Regarding an Airliner (Light & ball movement)

[HarleyM]

Homework Statement

Imagine that you are flying on an airliner on a long flight to Europe at a constant speed of 300 m/s

a) you throw a ball towards the back of the plane at 20 m/s. You then shine a beam of light towards the back of the plane. How will these two things-- the ball and light-- appear to move from the Earth's frame of reference

b) would you expect your watch to be affected by time dilation?

Homework Equations

Δt_m = Δt_s/√(1-v²/c²)

The Attempt at a Solution

a) The ball moves at 300-20 = 280 m/s forward
The light moves at c-v
3x10⁸-300=2.999997x10⁸ Confused here, this is an inertial frame of reference so is the speed of light a constant 3x10⁸ m/s or is 2.999997x10⁸ correct?

b) The plane does not move fast enough for time dilation to be noticed but it is occurring. The watch would not be able to detect the significantly small change in time dilation

 

[cupid.callin]

a) The ball moves at 300-20 = 280 m/s forward
The light moves at c-v
3x10⁸-300=2.999997x10⁸ Confused here, this is an inertial frame of reference so is the speed of light a constant 3x10⁸ m/s or is 2.999997x10⁸ correct?

Recall second postulate of STR
and for ball, you just applied classical eqn,, shouldn't you be using Lorentz transformations ?

 

[cupid.callin]

b) The plane does not move fast enough for time dilation to be noticed but it is occurring. The watch would not be able to detect the significantly small change in time dilation

Well i believe that's true !

 

[HarleyM]

Recall second postulate of STR
and for ball, you just applied classical eqn,, shouldn't you be using Lorentz transformations ?

second postulate states the constancy of the speed of light with regards to all inertial reference frames, therefore it moves at 3x10^8m/s I believe, and common sense fails me here.

I have no honest idea what Lorentz transformations are, it was not taught in this lesson as far as I know..

 

[cupid.callin]

I have no honest idea what Lorentz transformations are, it was not taught in this lesson as far as I know..

Using Lorentz transformation, you can transform velocity in any1 inertial frame from any other inertial frame which is moving at some velocity wrt previous frame ...
Here

 

[HarleyM]

That just made me really confused...

we weren't taught lorentz transformations in the lesson so idk if I should use them.. they seem straightforward and when I use u=v+u'/1+(vu'/c^2) I get 320 instead of 280..

as for the light part, am I correct I mean I just learned inertial frames and non-inertial frames today so I am very unsure of myself..

 

[cupid.callin]

That just made me really confused...

we weren't taught lorentz transformations in the lesson so idk if I should use them.. they seem straightforward and when I use u=v+u'/1+(vu'/c^2) I get 320 instead of 280..

as for the light part, am I correct I mean I just learned inertial frames and non-inertial frames today so I am very unsure of myself..

In this case, you will get same answer as in case of classical mechanics because the factor $\Large{\frac{vu'}{c^2}}$ comes out to be ≈ -10^-14 ... So if you write your answer upto 14 terms after decimal, you will see a change (pretty useless thing, i know!)

But will yes, if its no taught and the answer will have such a small difference then of course, you should use classical form,

And your first part is right that it will be c !