I am on a train travelling at 100 mph.I jump up from a standing position,why do i land on the same spot?Why have i not landed further down the train?

Because you’re also going 100 mph.

The train is moving at the same speed you are, 100 mph.

Are any of your relatives on the train?
Because they would also be going 100 mph. (Relatively speaking).

From your point of view, you have not moved any distance.

From someone who is not on the train though, you would have moved the same distance as the train.

Both of the objects have a speed of 100mph horizontally. Your standing vertical jump adds some vertical acceleration, no horizontal acceleration, thus the horizontal speeds remain the same.

Physics. In order to generate horizontal movement, there has to be an additional force applied. If you jump straight up while either standing still, or riding on a train at 100mph, there’s no additional force causing you to move horizontally along the ground or the floor of the train.

The Earth rotates at an incredible rate. Why don’t you fly eastward westward when you jump?

Even the air around you is keeping up with the train… in short, you have nothing to act as resistance against your body to change your velocity relative to the train. That’s why even lamps hanging from wires hang straight down.

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GA’s @Vinifera7 with a lurve high-five for posting the equivalent answer.

Well, it’s really the earth that’s moving. Not the train. (From your frame of reference).

inertia, objects in motion tend to stay in motion. one of the big three. You would slide back a hair, due to gravity, while the train keep rollin’, all night long.

Friction helps as well. Otherwise you’d be tumbling all over the place until you got stuck against something.

Sir Isaac Newton

It’s a little thing called relativity. You can also look at it as if you and the train are standing still and the rest of the world is moving at 100 mph. In fact, the planet we live on is revolving at about 900 miles an hour and you don’t see anyone flying off their feet, do you?

@AstroChuck Not counting me, of course. But I always do that

Most things stay in motion unless acted upon by an outside force. Physics lessons, of course, are the exception; they are immediately accelerated along a rearward vector the moment the fifth fundamental force, ‘grading’, ceases to be applied.

You’re not in the air long enough.

You don’t land in the same spot. But it’s slight.
When you jump, you are moving 100 mph, but you begin to slow down when you are in the air, since there the horizontal force of the train is no longer acting on you. When your feet hit the floor of the train again you might be moving 99.8 mph, and you have landed a fraction of a distance short of where you jumped, but it’s such a negliable amount that you don’t notice it.

If the compartment you are in has an open top, and you are capable of jumping 50 feet into the air, buy the time you land your horizontal motion will have slowed enough to notice.

Yo, Pete. Since you and the train are moving at the same speed, the train is never exerting any horizontal force on you. You do not slow down at all while you are in the air- note, an object in motion tends to stay in motion, unless acted upon by an outside force. The only force is gravity, acting directly downward. No horizontal force, thus no horizontal acceleration. The situation is exactly, and I mean that literally, as if the train were standing still. It is only if the train is accelerating that there is a difference. Neglecting air resistance (which is not even relevant here, as the air is also moving at the same speed as you, and air resistance is proportional to your relative velocity to the air, and acts along that vector), it would make no difference how high you jump; you will never have any horizontal velocity relative to the train.

Gravity does slow you down, genius.

It’s a simple vector quantity problem!

@steve6 Gravity’s vector is straight down and has no effect on your horizontal velocity.

it is straight down at the point the problem begins

Anyway, you should sit down. Your constant jumping is bothering the other passengers.

@Jayne The train’s engine is pulling the compartment that your in as well as you, but when you’re in the air that force ceases to You’re probably right.

@steve6 Unless the train is on an incline (not specified in the problem) the vector of gravity is normal to the motion of the train.

All you people are making a big assumption and obviously have not seen enough action movies…all are assuming that @emmaroid is inside the train. If in fact you are “on” the train in the literal sense, the situation is somewhat different. Perhaps your wide stance on the traintop allows you to remain in the same spot fighting the air resistance (tough at 100mph). If you jump, the resistance takes over, and you slow down quite a bit. You would indeed land further down the train and perhaps roll until you are hanging over the edge and your nemesis is standing above you laughing about how he’s about to kill you…but he’s not

@kfingerman: Ah, but you see, I am facing backwards, and the hail of bullets I unleash at my nemesis exerts a force on my body, by conservation of momentum, that is exactly equal in magnitude to the force caused by air resistance; thus, no net acceleration. booyakasha!

@steve6 And it continues to be straight down for the rest of the problem, too. Last I was aware, you can’t jump high enough for a train traveling at 100 mph to carry you off of the earth at a tangent before you come back down.

@Pete, just to clarify, any force the train exerts on you is exerted through friction. Friction is defined as acting against your motion relative to the surface, but you have no motion relative to the surface, and thus there can be no force of friction on you from the train, even when you are standing still. However, even disregarding the mechanism by which any force would be transmitted, the motion of two objects relative to the surroundings is irrelevant to their interactions with each other, so you might as well treat the situation as if the train and person were both standing still. (Incidentally, the engine is not really pulling the train, per se, it is simply compensating for any deceleration caused by friction with the tracks.)