If the vectors shown represent component vectors in Earth frame, then both get to the line at the same time, but only in Earth frame.
If, on the other hand, both Newton and Einstein are going straight to the side, but they each have an identical gun that shoots a bullet at the line at 0.2c, then Newton's bullet gets there first in Earth frame. Again, the answer is different in different frames.
Here are the answers I want to see. There is no definite answer in the special theory of relativity.
We often say that the light on Earth comes from the surface of the sun 8 minutes ago. If the sun is gone, the earth won't know until 8 minutes. So what is the truth of the facts? Did the sun just die or did it die 8 minutes ago?
If spacecraft A is moving away from the sun at a speed of c, will the sun not die?
Tom killed Jerry, but in a frame away from the earth at c speed, will Tom be innocent?
Because of the distance, it takes time for the light to reach the human eye. Classical physics tells us that when the relative speed of AB is v = 0, then the time required for the image of A to reach B's eyes is t = L / c. When AB moves to the opposite direction t = L / (c + v), when AB is far from each other t = L / (c- v), nothing more, it takes a certain time for the image to reach your eyes, but time does not change the existence of the fact.
The root cause of the uncertainty of the special relativity is the assumption that the speed of light is constant. Based on this premise, some mathematical formulas are derived, and these formulas are used to demonstrate that the speed of light is constant. It is like using A to prove that B is correct, then use B to prove that A is right.
All experiments used to prove that the speed of light is constant, they can be explained by the model of light being pulled by the gravitational field. The well-known Morley experiment can be easily explained using this model.
LIGO has observed the effect of gravitational waves on light. Such weak gravitational waves can affect the propagation of light on Earth. What other reasons do we have to deny the effect of gravitational fields on light?