An observer in frame $S'$ is moving to the right (+$x$-direction) at speed $u$ = 0.600c away from a stationary observer in frame S. The observer in $S'$ measures the speed $v'$ of a particle moving to the right away from her. What speed $v'$ does the observer in S measure for the particle if (a) $v'$ = 0.400c; (b) $v'$ = 0.900c; (c) $v'$ = 0.990c?
in the first part of this problem, we're going to find the speed off a particle mayor by the observer in his friend. So let the speed is we In order to calculate dispute, we apply the lost generation room off Einstein, which is written as we is equals to we prime bless you. Do I buy one? Plus we prime you pride you divide by C Square. We call it the question Number one. Now, by inserting well is into this equation, we can write this week's equals two 0.400 c lost that 0.600 See where this is the speed of light in wake you divide by one Plus here we can white 0.400 C into 0.600 c divide by C square. So from here we can wide the value For this we as well as equals toe 0.80 six c In part b of this problem, we are going to calculate the ah speed off the particle. What do you say we prime is equals to 0.900 c? So I did guess we need to find this we again let's put the values into equally number one we can write to ease equals two 0.900 C plus 0.600 C divide by one plus that 0.900 C into 0.600 city awarded by C Square. So from here, we can ride the value for this. We, as we is equals to, uh zero point 974 c In the third part of this problem party of this problem, we have to find the value for the survey when this way prime is equals to 0.990 c. So we again apply. Put the values into equation over one, uh for which we can write physicals to 0.990 C plus 0.6 00 c Divide by one plus, uh, here we can write 0.900 C into 0.6 00 c, divided by C square. So from here we can oil the value for this we, as we is equals to 0.9 97 c. So these results shows that that emancipate is that the speed of light in vacuum. And all these spirits which we have calculated here are less and see. Thank you.