What would happen if a ball flew through the open window of a car?

I asked a science teacher this question a while ago but I did not receive a clear answer. Now, I was hoping someone on this Physics site could shed some light on my conundrum,

I've been wondering for a long time what would happen if a ball flew into a car through an open window.

An example of this situation is detailed below in this excerpt from a novel I once wrote. The situation on the pages below highlights an event where two different scenarios occur and I was wondering which one would be more realistic.

Excerpt, pages 831-833:

The excerpt above may have been long and confusing. I also made this rough sketch of what it might look like:

In the situation on the left, the ball moves with the car while it is travelling in the car, and then flies out the other open window. In the situation on the right, the ball does not move with the car and keeps moving relative to the ground, and does not make it out the other window. The ball never touches anything in the car in either example.

So, which example represented here would likely occur? Is it possible that it could be either one? What would it depend on?

I've been doing a lot of thinking about this lately and I'm thoroughly befuddled. There were some other questions about flies in cars on this site but they didn't quite answer this question.

Hope this question makes sense - If anyone could help, that would be great! I looked online, but I couldn't find an example like this anywhere and I imagine this represents a unique conundrum,

• If the person that throws the ball has the same velocity as the car, the ball will pass through both windows (no air drag considered). Draw a sketch of velocity vectors and you'll understand. – QuantumBrick Jul 1 '16 at 15:21
• What would it depend on? It depends on car speed, ball speed, width of the window, lunch time, air resistance, etc. – lucas Jul 1 '16 at 15:24
• Brevity is the soul of physics :). Seriously, to get a better chance of an answer, you could trim your post down 90% and still get your point across. Otherwise, people will give up reading it 4 lines down. Best of luck with it though. – user108787 Jul 1 '16 at 15:43
• FYI, your sketch is inaccurate - it clearly shows the arrow moving sideways on the right-hand sketch, which I prosume is not the intention. – Steeven Jul 1 '16 at 16:20

I think your question is essentially a duplicate of Ball thrown from a moving train.

As QuantumBrick says in a comment :

If the person that throws the ball has the same velocity as the car, the ball will pass through both windows (no air drag considered).

So if both the thrower and the car are stationary on the ground, or the ball is thrown from a 2nd car which is moving alongside the 1st with the same speed, then the ball will pass through both windows. This is because all velocities are relative : if everything is moving at the same speed along the ground, this is equivalent to everything being stationary relative to the ground.

On the other hand if the thrower is stationary but the car is moving, then the ball will probably miss the 2nd window. The ball follows the same path relative to the ground as though the car is not there. It will go into one window, but by the time it reaches the other window the car will have moved forward. If the car is going fast enough the ball will probably miss the 2nd window.

The latter would also happen if the ball is thrown sideways from a car which is moving in the opposite direction into a stationary car. The ball moves forward with the same speed as the moving car, as well as sideways - so it moves diagonally relative to the ground. It enters one window of the stationary car but moves diagonally across the stationary car, and probably misses the far window.

[I didn't read your Exerpt. It was too long and mostly irrelevant.]

• If you didn't read the exerpt you'll never know if Gregg dies in the end. Will you be able to sleep at night? – QuantumBrick Jul 1 '16 at 17:03
• @QuantumBrick : OMG! Greg dies??? Hit by a ball thrown through the open window of his car? No, I won't sleep now. – sammy gerbil Jul 1 '16 at 17:08
• Forgot to begin my comment with spoiler alert. Sorry. I hope after some months of therapy you can get back to your life. – QuantumBrick Jul 1 '16 at 17:11

The important thing is that the neither the ball nor the car undergo an abrupt change in velocity as the ball enters and leaves the car. The ball may experience some acceleration as it encounters the air inside the car which will (to some extent: there will be a lot of complicated behaviour as the windows are open) be moving with the car and will therefore exert some force on the ball.

So let's do the normal physicist thing and ignore this: assume the car and ball are in a vacuum (your story now takes place on the Moon).

And let's look down on the situation from above and draw x and y axes. There is vertical (z) acceleration of the ball due to gravity but this won't matter in the x-y plane. And the frame of reference I'll pick is one stuck to the surface of the Moon, which for our purposes is inertial in the x-y plane: Newton's first law holds in x and y (in real life it is not quite inertial as the Moon is rotating, but I will ignore that).

Let's have the car be moving along the x axis with velocity $(c,0)$ and the ball is moving along the y axis with velocity $(0,b)$.

So what's the ball's velocity relative to the car? It's just $(-c,b)$: from the car's perspective it is moving backwards in x with the speed of the car and across the car with speed $b$. And this velocity remains constant because there is no force acting on the ball and the car's frame of reference is also inertial.

So the ball moves diagonally across the car: whether it makes it out the other side of the car depends on how large the windows are and how big $b$ and $c$ are.

In particular the ball doesn't somehow magically move with the car.

In real life there are two additional considerations:

• gravity -- the ball is falling as well and this means that it could, for instance, hit the car door on the way out;
• air resistance -- the ball will experience air resistance so even the x-y components of velocity will not be constant, and as it passes through the car the influence of air on it may be significant -- this is why I moved it to the Moon

The only way the ball can change it's sideways velocity from $0$ to $v_{car}$ (velocity of the car) is if something pull/pushes in it.

That pull or push is a (sideways) force $F$.

Let's look at the sideways forces that are possible here:

1. The ball could hit the car.
2. The ball could hit something that is already moving along with the car (like a passenger).
3. The ball could be moved by some wind pressure, by the air that is set in motion in/around the car.
4. ...

I can't think of more at the moment.

First of all, we are assuming that nothing is being hit, so points 1 and 2 are out. Point 3 could be relevant, as the air molecules that are moving along with the car inside the car are hitting the ball from the side as the ball crosses their path. I do though consider them to be far too light to give any considerable push, unless the ball is very close to hitting a surface, in which case air has less possibility to escape and the pressure thus is higher.

All in all - and especially if air is considered negligible (which is often is) - the ball will fly in a straight line, meaning that it will fly in through the first window but might not make it out the second (if it makes it naturally depends on the car speed and the ball speed).