A rocket ship flies past the earth at 87.0 % of the speed of light. Inside, an astronaut who is undergoing a physical examination is having his height measured while he is lying down parallel to the direction the rocket ship is moving.

If his height is measured to be 1.96 m by his doctor inside the ship, what height would a person watching this from earth measure for his height?

0.967m

Explanation:

Rocket's speed = 0.87c

Where c is speed of light in space

Since he's lying vertical his height becomes a length

Lenght l' = Lenght in rocket = 1.96m

Percieved Lenght on earth l =?

Due to relativistic effect his length will be reduced to;

l = l'(1-(v/c)^2)^0.5

l = 1.96(1-0.87^2)^0.5

l = 1.96(1-0.7569)^0.5

l = 1.96(0.2431)^0.5

l = 1.96(0.4931) = 0.967m

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.