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a) What is the proper length of the trip between these planets?

b) Find the length (in light-years) the red ship's science officer measures the trip to be, as

they travel.

2. Two events occur. Juan measures a time interval between the events of Δt=3.5 yrs and a distance between the events Δx=2.2 light-years.

a) Find the space-time interval Δs2.

b) Is this interval space-like, time-like, or light-like?

c) Will any observer observe the events as simultaneous? If so, how does that observer

move relative to Juan? If not, prove it.

3. A ruby laser at rest would emit light of wavelength 694 nm. You observe a moving ruby laser to emit light of wavelength 702 nm.

a) Is the laser moving toward you or away from you?

b) How fast?

4. A Borg spaceship is on its way to Earth. A Federation spaceship is sent from Earth at a speed of 0.9c to intercept it. The speed of the Borg ship relative to the Federation ship is 0.95c.

a) Draw a diagram, and label a positive direction.

b) What is the speed and direction of the Borg ship relative to the Earth?

*Does anyone have any idea about these four problems. One of these is going to be on my exam tomorrow. I'll be really and infact a million times thankful to anyone who helps me with these problems soon. very soon please because I'm not good in physics. I really need to do this exam good. Please somebody help!!!*