Why does an object far away looks like it's going very slow when it's going really fast? And then the object seems really fast when it's near me. I just started driving and I always try to find an answer but really can't. Thanks :)
I think Raza's question is more complicated (and fascinating) than the simple fact that objects that are close to you appear bigger than when they are far away. That's easily explained. Consider instead watching an airplane just before landing at an airport. I'm guessing it is probably travelling at 150 mph at least. That's 220 feet per second. So depending on the size of the airplane, it should be travelling more than once its own length per second. But when you look at it versus the background of sky and clouds, it sometimes appears to be moving much slower than that. Almost "hovering" in the sky sometimes. Part of this would be explained if the airplane was flying at an angle toward or away from you. But I've even noticed it when the airplane is travelling perpendicular to my line of sight. Optical illusion? Poor assessment of the facts on my part? Lack of stationary reference points behind the airplane??? Or is it something more fundamental with the spherical geometry of our field of vision, etc. ?? Paul
You're absolutely right. A Jumbo 747 generally lands at between 150 and 200 mph depending on the specific airport and local weather conditions at the time. But it certainly looks a lot slower than that.
I think your first response from Doc Al was as close to the truth as you'll ever get. Perspective. A distant object IS moving fast. just the angle that movement makes at your eye is smaller the further away the object is, so the angular speed is smaller. That's all you're saying really - the further away the object is from you, the smaller the angular speed is.
Just like the further away the object is from you, the smaller it appears to be. When you look up at the moon at night, you can cover it up with the tip of your finger, held out at arm's length. But the moon is really one heck of a lot bigger than your finger!
I'm curious as to how this changes apparent observations of the observer verses a stationary one. Not in terms of different physical phenomena, but in terms of how the geometry changes when moving at a constant speed, in short, what changes to the manner in which the moving observer makes his measurements in order to agree with the stationary observer. How is this different in the constant and accelerating frames of reference?
It is just about perspective. In this view, something far away is smaller because our eyes perceive them smaller due to our brain trying to interpret distance. Thus if distance is smaller, velocity would appear smaller. So it is just about our perception.
A graph of y=arctan(1/x) will help explain this: perceived angle versus distance.jpg A 747 aircraft appears to be slow, because our brains don't properly interpret the size of the aircraft, and mis-interpret the aircraft as being closer than it really is. Having a small jet fly side by side with the 747 helps reduce this affect. Experience watching aircraft reduces this effect.
On the graph, Y is the perceived angle in radians. X is the distance of the object in multiples of height. The perceived angle of the object is the angle determined by the ratio of height to distance. For my example, I set the viewer's eye level on the ground, and the perceived angle is relative to the horizon. This is arctan(height / distance). The graph shows the angle as radians, so the maximum angle perceived is pi/2 (vertically looking up at the top of the object as it passes directly by). For 0 distance, I used the limit as X approaches zero to get an angle of pi/2 (actually I used a 2 paramter arctan function, that takes x and y as seperate components, to eliminate division by zero for distance zero).
This is the cause of a large fraction of "credible" UFO sightings, including a famous one by the Mexican Air Force a while back that got months of discussion here before someone (not from here) figured it out. The fact that all motion is relative makes it utterly impossible to distinguish one motion from another without contextual clues about your velocity vs the velocity of what you are looking at. In this case, a couple of pilots "saw" some UFOs with an infrared camera. With no reference to size or distance, they concluded the "objects" were flying and maneuvering in close formation with them. It turned out that the "objects" were methane gas flames atop oil rigs some 40 miles away. Without knowing either distance or size, it is impossible to compute how the object is actually moving. The geometry is straightforward for relative motion: you just need to know 3 of the six pieces of information about a triangle (1 or 2 legs and 1 or 2 angles) to solve for the rest. At short angles/long distances, you can aproximate it pretty accurately with one angle and one leg. Perhaps the easiest (maybe the only) way to deal with this problem is to view all events from a top-down, stationary 3rd party perspective. You should at least know your own speed and using vectors, you can compute the "absolute" motion of another object with some relative motion information. The catch here is that if you don't know distance, you get a range of possible "absolute" distances vs speeds for a certain observed relative motion. For this particular case, a little bit of logic might have led someone to consider the possibility of the objects being stationary, or being on the surface, and using that information the problem could have been solved with ease. This is a common navigation problem, solved with a "maneuvering board": http://navsci.berkeley.edu/ns12b/lectures.htm Solving the problem during acceleration (such as in a turn) is only really possible (without some heavy math) during times of constant acceleration.