Time Dilation and aging Problem

[funkym0nkey]

Homework Statement

You fly 5000 km across the United States on an airliner at 250 m/s. You return two days later traveling at the same speed. How much less have you aged more then your friends at home.

Homework Equations

I think the time dilation equation is used:
delta_t= delta_t'/ sqrt(1-beta^2) where beta= v/c

The Attempt at a Solution

I have the solution from the solution manual but i'd like to know how they got to the answer, 1.39×10−8 s.

to find the delta t is the equation delta_t=delta_x/v used?

the beta is (250m/s)/(3.0*10^(8) m/s )

i keep getting 1.7 *10^-5 although the solution manual says this is incorrect.

Any advice is appreciated!

 

[jbae]

hi !

I've been so desperate to find the solution manual for mastering physics..!

Can you please tell me where you got it/?

or if it is possible, I would really really appreciate it if you could can it to my email, which is

guswns3310@hotmail.com

Thank you very much

 

[kerimek]

I would use the time dilation equation to solve this problem. The equation you mentioned, delta_t = delta_t' / sqrt(1-beta^2), is correct and should be used in this scenario.

First, we need to calculate the time dilation factor, which is represented by the term sqrt(1-beta^2). In this case, beta is equal to v/c, so we have beta = (250 m/s) / (3.0*10^8 m/s) = 8.33*10^-7.

Plugging this value into the equation, we get sqrt(1-(8.33*10^-7)^2) = 0.9999999999999999967.

Next, we need to calculate the time difference between the two flights. The distance traveled is 5000 km, which is equal to 5,000,000 m. Dividing this distance by the speed of the airliner (250 m/s), we get a time of 20,000 seconds.

Now, we can use the time dilation equation to calculate the time difference experienced by the traveler. delta_t = delta_t' / sqrt(1-beta^2) = 20,000 s / 0.9999999999999999967 = 20,000.000000000000000033 s.

Finally, we can subtract the time difference experienced by the traveler (20,000.000000000000000033 s) from the original time difference (20,000 s) to find the difference in aging between the traveler and their friends at home. This gives us 0.000000000000000033 s, which can be rounded to 1.39*10^-8 s.

In conclusion, the traveler would have aged 1.39*10^-8 s less than their friends at home due to time dilation caused by their high speed travel.