Printable View
imagine you're driving a car and looking out the side (OK, image you're a passenger)
the grass by the side of the road seems to be travelling quickly, while the trees far away seem to move slower.
if you're moving a a velocity v
and the grass is d1 metres away, then trees are d2 m away.
How do I find how quikly they seem to move?
Work with the angles. Consider a right triangle with one leg parallel to the direction of motion of the car. The other leg is perpendicular to the motion of the car and pointing directly at object. Calculate the angle of the hypotenuse when the car moves a standard distance.
For a spot on the distant horizon, the angle is very small, and the object seems to be almost stationary. For a telephone pole at the side of the road, the angle is obviously much larger.
Perhaps the rate of change of the angle might be a useful value for comparing the apparent speed of the object for a car moving at various speeds.
the grass should seem to be moving d2/d1 times faster than the trees. At what speed they seem to travel depends on what you project them on