Calculating Train Deceleration: Kid's Free Fall Time

[ejacques]

Homework Statement

when a high-speed train suddenly begins to decelerate at -5 (m/s^2), a kid sleeping on the upper bunk 3 meter above the floor falls off. where does he land?

Relevant Equations

y=-0.5*g*t^2

I think, since the train is decelerate the kid will fall off at free falling. the time for that is:
y=0.5*9.8*t² ⇒ t=√(2*y/g)=√(2*3/9.8)=0.8sec.

Now i think i need to find what is the distance the train is doing in this time, but i can't figure this out.

 

[kuruman]

How about writing equations for the positions of the kid and the train as a function of time? Take t = 0 when the deceleration starts. Unless the kid falls out an open window, it should land on the floor. The question is how far horizontally from the bed.

 

[pasmith]

Work in a frame in which the train is stationary. The kid is then initially at rest at $(x,y) = (0,3)$; how does that change when the train starts to decelerate?

Or you can work in an inertial frame in which the train accelerates to the left from rest at $5\, \mathrm{m}\,\mathrm{s}^{-2}.$

 

[ejacques]

I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.

 

[hmmm27]

I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.

So, run the equations with an unknown initial velocity $u$ for both train and kid, and see what happens.

 

[haruspex]

I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.

@pasmith gave you two approaches: a non inertial frame in which the train is stationary, or an inertial frame in which the train is initially stationary.

The second may be easier to understand. Imagine you are driving along next to the train at the same velocity. The decelerates but you don't.
You see the boy as falling vertically as the train accelerates backwards. This shows the initial velocity of the train is not relevant.

In the frame of the decelerating train, objects behave as though there is a kind of horizontal gravity in the forward direction. The train is stationary despite the frictional force. The boy will accelerate horizontally at 5m/s² (as well as vertically).

Of course, you could also work in the ground frame, putting the initial velocity of the train as an unknown. In the ensuing algebra, that unknown will cancel out.