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

Question

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:

To start with positive footing, the work of that employee was not wasted that evening. On the negative side, the very next pitch that Gregg rolled was slammed so hard by the kicker that C.1 thought the ball would explode in mid-air. Instead, something much worse happened; the ball flew with great speed towards the road, and at the very same moment, to the right, a red sedan emerged from behind a clump of pine trees speeding towards the ball. Would they intersect? C.1 was afraid that the ball would hit the red car. But after what happened next, C.1 considered that hitting the red car would have been better than what really did happen next. By this time, everyone was watching the ball. A blur of green flew over the sidewalk and the gutter, and just about when C.1 knew that the ball would surely smash the driver’s mirror, the ball flew right towards the window, and inside the car! They could all hear a shriek from the car as the driver freaked out. The driver’s window had been rolled down and the ball had somehow managed to fly inside the car! The car swerved and skidded before screeching to a halt, but not before taking out someone’s mailbox and narrowly avoiding a large tree as it came to a standstill on the lawn of the one-story house that still bore the ball on its roof. “Oh my goodness!” Gregg exclaimed after they had all closed their mouths. “I hope she’s alright!” Several employees dashed towards the road as fast as they could, sprinting with all their might until they reached the car. They began talking to the driver, and finally, they began sprinting back, right before the red car rolled off of the lawn, bounced over the curb, and continued on its way down the road. “Nearly took out her nose,” David explained as he reached the diamond again. “We explained what was going on and apologized, and she said that she had just suffered a fright that was all; she just rolled up her windows and drove away.” “Good to see that she has some common sense now,” Gregg lazily chuckled. “The ball, on the other hand, was not so lucky,” David said, handing Gregg a flat piece of green rubber. “It hit one of the knobs on the dashboard and popped. It’s very lucky that Marcia has inflated those extra balls, because we’ll need one.” The explanations concluded and the game resumed play. Several fielders guarded the road more than was necessary, and they kept their hands ready every time Gregg pitched the ball. Finally, the teams switched again, and Gregg’s team was up to kick again. Several home runs were scored, including Gregg’s, and he received a hearty applause from the team when he came running back in, his foot brushing over home plate just before a blur of green flew over the plate and bounced against the foul pole. Finally, it was C.1’s turn to kick. He imagined C.15’s face in the outfield, but quickly realized that he needed to think about someone he hated; not someone he loved. He finally decided on his deceased father and nodded his head towards the pitcher. Just before the ball came over the plate, C.1 slammed the ball for all it was worth. Without stopping to think, he shot off of the plate and began rounding the bases like his life depended on it. He kept one eye on the baseline and another on the ball, but just before he got to 3rd base, things got interesting, and C.1 stopped running to watch. The ball had indeed flown towards the air, but C.1 had kicked it with so much power, that it was still nearly 40 to 50 feet above the ground when it passed the infield. One of the men in the outfield made a jump for the ball, but it flew several feet above his hand and… Just as C.1 thought that it would just land in the street and that would be the end of it, another car came rocketed out of the blue from nowhere, speeding towards the intersection where the ball and the driver had previously collided earlier that game. C.1’s eyes filled with horror, and just as he braced himself for the worst, a very interesting thing happened. First, the ball did indeed fly through the driver’s window, but instead of getting stuck inside the car as it would have if it were not for the driver rolling all of the car’s windows down, it flew right out of the other window on the passenger side. But before everyone could express their awe to each other, another interesting thing happened. Right after the ball flew out of the car’s window, the car continued down the street, on its way as if nothing had happened. C.1 was confused at first, but decided that it must have happened so fast that the driver would definitely not have remembered anything but a greenish blur in front of his or her face. But this was soon driven out of his mind; for the next moment, they were all distracted by the sound of a garage door closing! They all turned to look; the garage door of the house right in front of where the car had been had just started closing, and just before the ball reached the ground, and just before the garage door fully closed, the ball flew under the garage door and into the garage, just before the garage door reached the ground! Gregg’s hand flew up to his mouth in horror, as did several others. Clearly, nothing like this had ever happened before at a kickball game. Gregg called for time-out, and soon, Willis, Gregg, David, and C.1 were sprinting as fast as they could towards the house that the ball was now somewhere in. At last, they quickly crossed the street over to the house that the ball was in. A large maple tree bordered by an oak occupied the majority of the front yard, with much of its many upper branches hanging over into the street as if sheltering it from the house. They hurried up the front walk which was to the right of the garage; jumping the porch steps two at a time, and Gregg rang the doorbell before the rest of them had reached the door. It was several rings later before anyone answered the door. When the door opened, it revealed a lady with brown hair likely in her mid to late forties. Without wasting any time, Gregg quickly began to explain what had just happened, and the lady nodded and said, “Hmm…hmm… OK…” from time to time until Gregg had completed his explanation. “So it’s in the garage, you say?” she asked finally. “That it is, ma’am,” Gregg kindly replied. The lady beckoned them into the house and they followed her. They turned left to go down a short hallway into a dimly lit room before the lady unlocked a door to their left and they peered into the dark garage, its only light coming through a window in the attic of the garage. Underneath a wheelbarrow, in plain view, was the green kickball, without so much as a scratch upon it. “Thank you, ma’am,” Gregg replied, as he fetched the ball and they turned to leave the house. The lady waved goodbye and they hurried back to the baseball diamond.

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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,

Answer 1

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.]

Answer 2

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

Answer 3

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).