Time Interval between Rocket Explosions for Spaceship Tripulant

[Jalo]

Homework Statement

Two students on the ground, separated 100m from each other, launch one rocket each vertically. The rocket explode at the same time for an observer, on the ground, that's midway between the rocket explosion. At the exact time the observer sees the rockets exploding a spaceship flies over his head, horizontally, at a speed of 0.7c. The ship length as seen by the observer is 15m.

(c)How much time goes by, to a tripulant of the spaceship, for the ship to complete the 100m between the two students?
(d)For a tripulant of the spaceship is the explosion of the rockets simultaneous? What's the time interval? (time between the first rocket explosion and the second, as seen by the tripulant)

Homework Equations

After solving the first two questions I've reached this data:
Actual distance between the two students = 71.4m
Spaceship length as measured by the tripulant = 21m

As to question (c) I used the equation t=d/v to solve it.

The Attempt at a Solution

(c) I think I've done her correctly. I've simply divided the length between the two students as seen by a tripulant in a ship by her speed:
t=71.4/0.7c=3.4*10^-7

(d) I know the explosions are not simultaneous, however I have no idea how I'm supposed to measure the time interval between the two explosions... If anyone could give me some hint, or some equation that could help me i'd be grateful. I've readen the whole relativity chapter of Serway's Physics for Scientists looking for something to help me without any luck.

Thanks, and a happy new year to everyone.

 

[SammyS]

Homework Statement

Two students on the ground, separated 100m from each other, launch one rocket each vertically. The rocket explode at the same time for an observer, on the ground, that's midway between the rocket explosion. At the exact time the observer sees the rockets exploding a spaceship flies over his head, horizontally, at a speed of 0.7c. The ship length as seen by the observer is 15m.

(c)How much time goes by, to a tripulant of the spaceship, for the ship to complete the 100m between the two students?
(d)For a tripulant of the spaceship is the explosion of the rockets simultaneous? What's the time interval? (time between the first rocket explosion and the second, as seen by the tripulant)

Homework Equations

After solving the first two questions I've reached this data:
Actual size of the ship = 71.4m
Spaceship length as measured by the tripulant = 21m

As to question (c) I used the equation t=d/v to solve it.

The Attempt at a Solution

(c) I think I've done her correctly. I've simply divided the length between the two students as seen by a tripulant in a ship by her speed:
t=71.4/0.7c=3.4*10^-7

(d) I know the explosions are not simultaneous, however I have no idea how I'm supposed to measure the time interval between the two explosions... If anyone could give me some hint, or some equation that could help me i'd be grateful. I've read the whole relativity chapter of Serway's Physics for Scientists looking for something to help me without any luck.

Thanks, and a happy new year to everyone.

You wrote: "Actual size of the ship = 71.4m" This must be a typo. The "proper" length of the ship is the 21 meters, as seen by tripulant. It appears that the tripulant will see the two students as being about 71.4 meters apart. The two rocket explosions will be separated up the same amount, as seen by the crew-member.

 

[Jalo]

You wrote: "Actual size of the ship = 71.4m" This must be a typo. The "proper" length of the ship is the 21 meters, as seen by tripulant. It appears that the tripulant will see the two students as being about 71.4 meters apart. The two rocket explosions will be separated up the same amount, as seen by the crew-member.

Yes, it was a typo, thanks for bringing it to my attention :)