Formula to calculate the time it takes 2 objects to meet?

[Munku]

Basically, you have X distance, and two objects moving toward one another at Y speeds. What formula would I use to calculate the time it takes both objects to meet? I know this is something simple but I can't for the life of me think of how to do it nor can I find it on the web.

[Munku]

Man.. It seems every time I post a question it hits me 5 mins later..

I never thought of taking a set of numbers I knew, writing a formula, and then solving for time! BLEH!

[dlish]

the way i see it.. say you have 100km between two objects...

x is moving in a car at 60km/hr
y is moving in a car at 60km/hr, both heading towards each other

the formula would some something like

time = distance/velocity

distance (100km in this case)
____________________
(x speed + y speed)


= 100/120
=0.83hrs
times by 60 to convert to minutes

=50 minutes

i dunno..i only did the second lowest maths at school.. maybe im wrong

[Munku]

Yeah you're right, that's what I did. Except I wasn't looking at it that way which was causing some real problems in my head.

[Martian]

The understanding of it is based in the concept of velocity. We use velocity against a fixed object (the Earth, usually), so we tend to think of it in very finite terms. An object's absolute velocity (say, a train leaving location x, to use the cliche) may be 120 km/h. However, if another object is heading towards it at 100 km/h, it's velocity relative to that object is actually 220 km/h. Once you understand that, it's a simple time/distance/velocity calculation.

You can do funny things with that knowledge. For example, if you're riding the train that's going 120 km/h and you throw a ball off the back at 30 km/h, the ball will appear to you to be travelling away from you at 30 km/h. However, to a stationary observer, the ball is actually moving in the same direction as you at 90 km/h.

Velocities are fun stuff.

[BadNick]

Originally Posted by Martian

Velocities are fun stuff.

I just don't have "feelings" about velocities ...maybe I'm jaded. I need acceleration to have fun!

[Dilbert1234567]

Originally Posted by Martian

You can do funny things with that knowledge. For example, if you're riding the train that's going 120 km/h and you throw a ball off the back at 30 km/h, the ball will appear to you to be travelling away from you at 30 km/h. However, to a stationary observer, the ball is actually moving in the same direction as you at 90 km/h.
Velocities are fun stuff.

or if you throw it at the observer, you can hit him with it at 150 kph (ouch)

[Silvy]

Originally Posted by Dilbert1234567

or if you throw it at the observer, you can hit him with it at 150 kph (ouch)

Which comes to another interesting concept, the speed of light.
If the speed of light is a fixed value, how fast is light on the train going?

If it is relative to the train, then to an observer outside light is going faster than the speed of light.
If it is not relative to the train (because of its fixed universal speed) then to a passenger on the train, the speed of the light will have slowed.
(or: is light that is -on the train- going at relative speed to the train, and light that -exits the train- going at relative speed to the ground. Which means that at the front window of the train there should be an increasing volume of light)

I expect someone to be able to explain it clearly, but it's always been a nice mental puzzle for me.

[Martian]

Speed of light, eh? Now we're getting into some Einstein type shit.

He noticed the same thing you did. Namely, light moves at the same relative speed as an observer on the train and an observer on the ground. It was kind of controversial at the time, since the only way that could be true is if time was relative.

Think of it this way - we express speed as an integer, but it's actually a fraction - speed is our way of measuring distance divided by time taken to traverse it. Normally and prior to Einstein it was assumed that the bottom number - the per hour, per second or per minute part - never changed. An hour was the same whether I was going 100 mph, 1000 mph or 1 000 000 mph. The hour was always the same; the only part that changed was how far I managed to get. That works for relatively small numbers of the sort we use in our day to day lives (often referred to as Newtonian physics, because they use Isaac Newton's less accurate but 'good enough' formulae), but when we get up closer to the speed of light, it starts to become less true. Finally, at the speed of light itself, the distance is the number that never changes; no matter where the person seeing it is or how fast they're going, the top number is always the same (299 792 458 m/s, or about a bit under 700 000 000 mph). That's tricky, since in order for the top number to stay the same and for the equation to still work, the bottom number has to change - so an hour is no longer an hour. Or rather it is, but my hour at 100 000 000 mph and yours at 1 mph aren't the same length of time.

This, again, leads to some funky stuff. For example, time passes faster at the top of a mountain than it does at the base, since the top of the mountain is moving faster due to the Earth's rotation. The difference is very small, but it's enough that a sufficiently accurate clock can measure it; this is one of the tests that was used to verify the theory, substituting a convenient water tower for a mountain since physicists aren't generally known for their mountaineering abilities.

Does that help you make sense of it?

EDIT -

Originally Posted by Dilbert1234567

or if you throw it at the observer, you can hit him with it at 150 kph (ouch)

This is true, sort of. In order for your throwing the ball at 30 km/h to give it a total velocity of 150 km/h, you'd have to throw it off the front in the same direction the train is going. In that case, for the ball to hit the observer at 150 km/h he'd have to be directly in front the train; I'd propose that if this is the case the ball is really the least of his problems.