Math Is Fun Forum

JaneFairfax

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Registered: 2007-02-23

Posts: 6,868

Relative velocity (a physical demonstration)

Suppose a vehicle is travelling at 100 kmh[sup]−1[/sup] relative to an observer. A tennis ball is lauched from the vehicle at 100 kmh[sup]−1[/sup] relative to the vehicle in the opposite direction to the vehicle’s motion. What is the velocity of the tennis ball relative to the observer?

Of course you know your physics, so you know the answer – namely, zero. And here is an interesting experimental demonstration!

http://www.koreus.com/video/experience- … ennis.html

In the superslow-motion replay right at the end, you can really see what happened: the tennis ball simply dropped vertically to the ground! It did bounce forward after it hit the ground, but that was due to its own spin. While it was in the air, there was no horizontal translational displacement whatsoever.

mathsyperson

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Registered: 2005-06-22

Posts: 4,900

Re: Relative velocity (a physical demonstration)

It seems like it was moving forward a tiny bit whilst in the air. Still, when dealing with those kinds of speeds it's negligible though. The discrepancy was probably just a bit of friction in the barrel or some air resistance.

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Identity

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Registered: 2007-04-18

Posts: 934

Re: Relative velocity (a physical demonstration)

But it's impossible that it just drops to the ground, because first it must accelerate to 100kmh-¹, right?

Ricky

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Registered: 2005-12-04

Posts: 3,791

Re: Relative velocity (a physical demonstration)

You have to remember there are tons of negligible forces.  For example, the truck displaces air while it travels and so there is air rushing in towards the truck from the back which would push the ball forward.  Wind of course is another one.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Ricky

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Registered: 2005-12-04

Posts: 3,791

Re: Relative velocity (a physical demonstration)

I don't believe that launching machine should create much, if any, spin on the ball.  So I'm really curious at how the ball took such a sharp jump forward.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Relative velocity (a physical demonstration)

Perhaps the ball merely retained some of its initial velocity. Using that kind of speed meter in the car can lead to major inaccuracies.

Ricky

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Registered: 2005-12-04

Posts: 3,791

Re: Relative velocity (a physical demonstration)

Perhaps the ball merely retained some of its initial velocity. Using that kind of speed meter in the car can lead to major inaccuracies.

From the video, it shows the ball has almost no forward velocity while falling, and sharply accelerates when it hits the group.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

luca-deltodesco

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Registered: 2006-05-05

Posts: 1,470

Re: Relative velocity (a physical demonstration)

yeh, the only way it can jump foward like that is with extreme spin, perhaps to do with the air currents behind truck?

as an interesting sidenote, although still related, if you're on a vessel travelling near speed of light, and you walk to the front, do you overcome the speed of light?

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JaneFairfax

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Registered: 2007-02-23

Posts: 6,868

Re: Relative velocity (a physical demonstration)

In special relativity, the equation of relative motion is

Ricky

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Registered: 2005-12-04

Posts: 3,791

Re: Relative velocity (a physical demonstration)

Assuming the launching apparatus was 6 feet off the ground, the truck was 0.1701 meters away when the ball hit the ground.  An interesting hypothesis, luca.  Any suggestions on how to test it?

On the other hand, the ball accelerated forward the moment it hit the ground.  I find that far too coincidental to attribute to wind currents.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Laterally Speaking

Real Member

Registered: 2007-05-21

Posts: 356

Re: Relative velocity (a physical demonstration)

If you look closely at the video, you can see that, while in the air, the ball travels forward (in the same direction as the truck) about 3/4'. Also, the type of launcher used, if there is the slightest speed difference between the upper and lower wheels, could easily put a fair amount of spin on the ball. It is, nonetheless, quite odd that the ball should bounce so far forward.

Also on the video, it seems that the truck is much farther away than 17, 01 cm away when the ball hit the ground.

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Ricky

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Registered: 2005-12-04

Posts: 3,791

Re: Relative velocity (a physical demonstration)

There are two assumptions on my part: 1. Air resistance 2. Angle of launch.  Short of an updraft of more than 20mph, air resistance should be negligible.  So perhaps the angle of launch is off.

Assume the that the car is actually going at 100km/h and that the ball launcher launches at the same speed.  Also, assume that the ball landed 1/3 meter from where it was launched.  Calculate the forward speed of the ball relative to the camera, use this to find the angle it was launched from, and then use this to calculate how far the ball should be from the truck when it hits the ground.

It should be noted that you can assume that the angle is either up or down to make it fit with the distance traveled.  But we already found that if we assume it is parallel to the ground, the ball is too far away.  So we need the time it takes for the ball to fall to be greater, and thus, the angle must go up.

Anyone want to give it a shot?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Laterally Speaking

Real Member

Registered: 2007-05-21

Posts: 356

Re: Relative velocity (a physical demonstration)

It's also probable that the speed was slightly influence by the fact that it was traveling at 100km/h at a slight angle, rather than perfectly parallel to the road, thus the fact that the ball didn't fall straight down.

The angular discrepancy could also have to do with a slight difference in speed between the two wheels. If the upper one is spinning faster than the lower one, it would seem that the launcher is at an upwards angle.

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"Knowledge is directly proportional to the amount of equipment ruined."
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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Relative velocity (a physical demonstration)

I still think spin is what caused the ball to bounce forward that much. If the launcher pushed the ball below centre while launching it, it would impart the necessary bottom spin that would enable the ball to bounce forward – and bearing in mind that the balled has to be ejected at 100 kmh[sup]−1[/sup] relative to the launcher (that’s between 60 and 70 mph for those of you from another planet), you can see that any spin imparted to the ball this way can be considerable.

In fact, even a little spin can do a lot to any ball – as anyone who has watched or played cricket will readily testify. Any of you ever watch Shane Warne or Mutthiah Muralitharan bowling?

Laterally Speaking

Real Member

Registered: 2007-05-21

Posts: 356

Re: Relative velocity (a physical demonstration)

Also, the ball used is not a tennis ball, but a golf ball, which wouldn't create as much friction as a tennis ball, so the spin would have to be more accentuated to make as much of a difference.

However, I agree that the spin is the most likely contributor to the angled bounce.

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"Knowledge is directly proportional to the amount of equipment ruined."
"This woman painted a picture of me; she was clearly a psychopath"