I have trouble understanding why time dilation occurs for objects moving towards you at no angle.
There are two example in my physics textbook:
A woman is on a moving train holding two light bulbs in her hands. As she moves across the platform, they flash. To her, the flashes are simultaneous. To an observer on the platform, the closest one flashes first. This makes sense to me as one flash has less distance to travel.
An observer on Earth sees a meteor travelling directly toward Earth. Classically, to calculate how long it takes the meteor to hit Earth, divide the distance between Earth and the meteor by velocity. Makes sense.
But why does special relativity tell you to multiply the time it takes for impact by $\gamma$? Why is the time longer for the person when the distance in both classical and special relativity is the same?