What Trajectory Does an Apple Take When Dropped in a Decelerating Train?

[Chip90]

Homework Statement

A train slows down with constant deceleration a. A boy in the train drops an apple.

What path does the boy observe the apple to take? Find an equation y=f(x) to describe the trajectory of the apple.

Also, if the original height of the apple was yo, calculate how far it is from the child when it hits the floor.

Homework Equations

Projectile Motion equations again?

The Attempt at a Solution

For part a, I think the answer is x=Vox T

but that is not in terms of y.

For the second part, I am not sure what to use. maybe y=-0.5 g t^2 + Vo T ?

TIA

 

[vela]

You need to understand the implication of the first sentence. How does the train's deceleration come into play in this problem?

 

[Chip90]

well the forces on the ball are:

mg which is point down in y-axis and there is acceleration in negative direction (ie left since i chose --> to be +)

 

[vela]

OK, so what you're saying is in the frame of the boy/train, there appears to be a horizontal force on the ball, which causes it to accelerate horizontally, in addition to the usual vertical force and acceleration due to gravity. (This horizontal force is a fictitious force. It's only there because the reference frame of the boy/train is non-inertial because the train is decelerating.)

So which direction is the train moving? In the positive direction or the negative direction? Which direction is its acceleration? I'm just asking these questions to clarify exactly what you're thinking, so I know we both have the same picture of what's going on in our heads.

 

[Chip90]

the train is moving in the positive direction, but is slowing down and this is accelerating in the negative direction.

 

[vela]

If the acceleration of the train is in the negative direction, then from the point of view of the boy, the ball will appear to accelerate forward because it isn't slowing down like the train. So the horizontal component of the ball's acceleration should be positive, not negative like you said back in post #3. Make sense?

 

[Chip90]

ok that makes sense, so the eq would be

Ffict=ma

since the fictitious force acts in the opposite direction and a is + for the ball?

 

[vela]

Yes, but the force is really a side issue. What you need to solve the problem is the acceleration of the ball in the train's rest frame. You have both components now, so you can move onto calculating the motion of the ball.

 

[issacnewton]

the trajectory of the apple in the train will be y=(-g/a)x where origin of the coordinate system in the train is the point of release and 'a' is the magnitude of the deceleration of the train. so according to the passengers in the train, the apple falls in a straight line with the slope (-g/a)