Question

Short answer

Step (a). event 1 : friend will leave the Los Angeles

Step (b). The friend in the flight will measure the proper time.

Step (c). Your friend will measure the shorter time.

Step-by-step solution

Part (a) Step 1 : Given Information

It is given that your friend will travel from the Los Angeles to New York .

We need to find the two events.

Part(a) Step 2 : Simplify

Event 1: Your friend take off from the Los Angles.

Event 2: Your friend land on the New York.

Part (b) Step 1 : Given Information

It is given , that your friend will travel from the Los Angeles to New York.

We need to find that who will measure the proper time.

Part (b) Step 2 : Simplify 

Simplify

Using Lorentz Transformation,

Where,

t= time for the assistance

t'= time for your friend

v= velocity of flight

x= distance between the two cities.
Since the proper time is in frame of your friend then it will measure the proper time.

Part (c) Step 1 : Given Information

We have given, that your friend will travel from the Los Angeles to New York.

We have to find the who will measure the shorter time.

Part(c) Step 2 : Simplify

Using Lorentz transformation,

the time observed by the assistance is equal to the time observed by your friend with some multiple factor.

Then we can say that the time of your friend is less then the time for the your assistance since the value of the factor will be always greater then 0.