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Tiresias · Mar 5, 2007, 02:16 AM

A bee flying north hits the windscreen of your southbound car. The bee's trajectory has therefore been reversed, but the car is moving at a constant speed of 80 kph.

How is it possible for the bee to reverse directions without there being a momentary pause in its velocity?

Mithras · Mar 5, 2007, 06:45 AM

Velocity does cross the point '0' momentarily. You can call that a pause if you like.

f1000 · 08:19 PM

Originally Posted by Tiresias

A bee flying north hits the windscreen of your southbound car. The bee's trajectory has therefore been reversed, but the car is moving at a constant speed of 80 kph.

How is it possible for the bee to reverse directions without there being a momentary pause in its velocity?

It can't: as Mithras said, the bee, at least in portions, must momentarily pause in velocity. What happens is that the particles comprising both the bee and the windshield distort to allow for rapid, continuous deceleration. This occurs so quickly and on such a small scale that you can't see it with the naked eye. High-speed video of a ball hitting a baseball bat, for example, reveals a significant amount of distortion in both the ball and the bat during impact.

Distortion of bat and ball at the point of impact.

Bending of the bat shortly after impact.

Moreover, assuming an elastic collision and no additional energy input into the system, conservation of momentum dictates that the car must also be slowed down by some infinitesimal amount due to the impact.

d4nth3m4n · 02:40 PM

that's like saying that if you throw a ball up it won't change direction and come back down.

try again.

Gossamer · Mar 5, 2007, 03:13 PM

Originally Posted by d4nth3m4n

that's like saying that if you throw a ball up it won't change direction and come back down.

try again.

Wanna bet how many pages this one will hit?

d4nth3m4n · Mar 5, 2007, 03:33 PM

Originally Posted by Gossamer

Wanna bet how many pages this one will hit?

oh god, better be less than 3. i'd like to hang on to my shred of faith in 'NN not being populated by the unwashed everyman, thankyouverymuch.

climber · Mar 5, 2007, 04:15 PM

I am not sure that the bee actually will cross the point of zero velocity. Unless the objects are theoretically 180 degrees opposite in trajectory at impact. If the bee was heading slightly off course then the velocity would approach zero, but not actually reach it. Think about a bee that is traveling 90 degrees sideways. It's direction would just be changed.

d4nth3m4n · Mar 5, 2007, 04:18 PM

what's the last thing going through a bee's head when it hits a windshield?

it's butt.

design219 · Mar 5, 2007, 05:11 PM

Originally Posted by d4nth3m4n

what's the last thing going through a bee's head when it hits a windshield?

it's butt.

HAAAAAAA. The first laugh I've had all day. Thank you.

f1000 · Mar 5, 2007, 05:14 PM

Originally Posted by climber

I am not sure that the bee actually will cross the point of zero velocity. Unless the objects are theoretically 180 degrees opposite in trajectory at impact. If the bee was heading slightly off course then the velocity would approach zero, but not actually reach it. Think about a bee that is traveling 90 degrees sideways. It's direction would just be changed.

A bee that is traveling perpendicular to the direction of the car already has a component vector of zero in the direction of the car. In any case, you're still thinking in terms of point particles, which are only approximations of real objects.

It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt.
-- Mark Twain

Snow-i · Mar 5, 2007, 05:22 PM

Originally Posted by climber

I am not sure that the bee actually will cross the point of zero velocity. Unless the objects are theoretically 180 degrees opposite in trajectory at impact. If the bee was heading slightly off course then the velocity would approach zero, but not actually reach it. Think about a bee that is traveling 90 degrees sideways. It's direction would just be changed.

He's right in what he's saying, assuming a real world situation where the bee would not bounce straight back (if any part of it bounced at all, if not then the point is moot).

However it is assumed from interpreting the OP's question that indeed it is a hypothetical straight on collision (no offset). Where for an instant the equation(function? my calc's a bit rusty) for the bee's location would have a 1st derivative equal to 0 but a 2nd and 3rd derivative much greater than 0. In other words, the velocity would be zero but the bee would be accelerating.

design219 · Mar 5, 2007, 05:28 PM

I think bees are kind of squishy. I would imagine the internal gooey bits would all go at different angles.

climber · Mar 5, 2007, 09:46 PM

Originally Posted by f1000

A bee that is traveling perpendicular to the direction of the car already has a component vector of zero in the direction of the car. In any case, you're still thinking in terms of point particles, which are only approximations of real objects.

It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt.
-- Mark Twain

The bee will begin accelerating on the new "component vector" before the bee finishes the deceleration on the old trajectory... Get it now?

climber · Mar 5, 2007, 09:50 PM

Originally Posted by d4nth3m4n

that's like saying that if you throw a ball up it won't change direction and come back down.

try again.

This is an interesting analogy. But in part illustrates my point. In real life the ball thrown upwards will never reach a velocity of zero. It will curve slightly and have a slight horizontal movement even at max altitude.

Gossamer · Mar 5, 2007, 09:54 PM

Originally Posted by climber

This is an interesting analogy. But in part illustrates my point. In real life the ball thrown upwards will never reach a velocity of zero. It will curve slightly and have a slight horizontal movement even at max altitude.

That's why you separate horizontal and vertical velocities. At some point the vertical velocity will be zero because the acceleration is a constant 9.81m/s^2 downward, but throughout the entire trajectory the horizontal velocity remains constant (ideally) because there's no outside force in that direction.

Tiresias · Mar 5, 2007, 09:56 PM

Originally Posted by d4nth3m4n

that's like saying that if you throw a ball up it won't change direction and come back down.

try again.

It's nothing like that.

climber · Mar 5, 2007, 10:00 PM

Originally Posted by Gossamer

That's why you separate horizontal and vertical velocities. At some point the vertical velocity will be zero because the acceleration is a constant 9.81m/s^2 downward, but throughout the entire trajectory the horizontal velocity remains constant (ideally) because there's no outside force in that direction.

I am not entirely sure of your point. It has been over 20 years since I studied this stuff, and my background is more engineering than mathematics. My answer was mostly intuitive, hence my original statement " I am not sure".

If there is a horizontal velocity. Then the object is still moving. At least relative to a fixed point on the ground.

Gossamer · Mar 5, 2007, 10:06 PM

Originally Posted by climber

I am not entirely sure of your point. It has been over 20 years since I studied this stuff, and my background is more engineering than mathematics. My answer was mostly intuitive, hence my original statement " I am not sure".

If there is a horizontal velocity. Then the object is still moving. At least relative to a fixed point on the ground.

The question asks how it's possible for the bee to reverse directions without a momentary pause in its direction. If it's velocity is perfectly parallel to the car's velocity, then it does indeed have zero velocity for a very short time, just as a ball will have zero velocity if it is moving perfectly upward without any horizontal component of velocity.

climber · Mar 5, 2007, 10:30 PM

Originally Posted by Gossamer

The question asks how it's possible for the bee to reverse directions without a momentary pause in its direction. If it's velocity is perfectly parallel to the car's velocity, then it does indeed have zero velocity for a very short time, just as a ball will have zero velocity if it is moving perfectly upward without any horizontal component of velocity.

Ok, I understand what you are saying. And I agree, as long as no horizontal component is involved velocity will reach zero. Again relative to a spot on the ground. But if there is any perpendicular motion then the result is different.

Also think about a windshield that is angled (as any car is). It will introduce a sideways or offset motion or velocity before the bee has had time to decelerate to zero. In other words, the same force that is decelerating the bee from its original trajectory also introduces a force pushing the bee upwards (assuming the windshield is tilted to break the wind). These forces will occur simultaneously.

f1000 · Mar 5, 2007, 10:44 PM

Originally Posted by climber

The bee will begin accelerating on the new "component vector" before the bee finishes the deceleration on the old trajectory... Get it now?

You've either never learned or completely forgotten how to work with orthogonal vectors when computing elastic collisions. Your bee never decelerates on its old trajectory, since the old trajectory was perfectly orthogonal to that of the car. Instead, your bee will pick up a velocity component that is parallel to that of the moving car and almost double in magnitude; hence, its new speed would be equal to sqrt[(old speed)^2 + (2 x car's speed)^2].

f1000 · Mar 5, 2007, 10:48 PM

Originally Posted by climber

Ok, I understand what you are saying. And I agree, as long as no horizontal component is involved velocity will reach zero. Again relative to a spot on the ground. But if there is any perpendicular motion then the result is different.

Also think about a windshield that is angled (as any car is). It will introduce a sideways or offset motion or velocity before the bee has had time to decelerate to zero. In other words, the same force that is decelerating the bee from its original trajectory also introduces a force pushing the bee upwards (assuming the windshield is tilted to break the wind). These forces will occur simultaneously.

Once again you fail to properly decompose vectors. If you were to look at the situation from above, the bee would appear to pause momentarily before reversing direction; only this time, the bee would acquire a velocity component normal to the ground.

SpaceMonkey · Mar 5, 2007, 10:52 PM

Okay, now imagine that the bee hits a giant treadmill...

climber · Mar 5, 2007, 10:59 PM

Originally Posted by f1000

You've either never learned or completely forgotten how to work with orthogonal vectors when computing elastic collisions. Your bee never decelerates on its old trajectory, since the old trajectory was perfectly orthogonal to that of the car. Instead, your bee will pick up a velocity component that is parallel to that of the moving car and almost double in magnitude; hence, its new speed would be equal to sqrt[(old speed)^2 + (2 x car's speed)^2].

Well unless I go grab my old textbooks out... and as I said it has been a very long time. I am not trying to be argue, or act like the expert. I would have a hard time doing the math on paper, let alone in my head. Right now, I am trying to understand what your point is. Are you saying even a bee that is traveling from the side would have a velocity of zero (relative to the ground) at some point in time after such a collision?

climber · Mar 5, 2007, 11:04 PM

Originally Posted by f1000

Once again you fail to properly decompose vectors. If you were to look at the situation from above, the bee would appear to pause momentarily before reversing direction; only this time, the bee would acquire a velocity component normal to the ground.

Just because the bee would appear to pause, does not make it true. Would there be a vertical component (from an angled windshield) in the bees motion while it was being redirected from north to south? yes or no???

Gossamer · Mar 5, 2007, 11:08 PM

Originally Posted by SpaceMonkey

Okay, now imagine that the bee hits a giant treadmill...

Nooooooooooo!

f1000 · 11:18 PM

Originally Posted by climber

Well unless I go grab my old textbooks out... and as I said it has been a very long time. I am not trying to be argue, or act like the expert. I would have a hard time doing the math on paper, let alone in my head. Right now, I am trying to understand what your point is. Are you saying even a bee that is traveling from the side would have a velocity of zero (relative to the ground) at some point in time after such a collision?

I see what you're asking. Yes, I think you're right to conclude that the speed of the bee relative to the ground would never go to zero in your example; instead, the bee would trace some sort of infinitesimally small radius arc during its fleeting electrostatic interaction with the windshield and then head off into a new direction. The closest analogy I can think of would be the slingshoting of satellites around planetary bodies, but at an atomic scale.

climber · Mar 5, 2007, 11:17 PM

Originally Posted by SpaceMonkey

Okay, now imagine that the bee hits a giant treadmill...

A bee is capable of a vertical takeoff, and as such it could be airborne before that particular feedback loop is entered. It also does not have wheels.