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# Inertial observer O´ moves at speed v.

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A.1 Inertial observer O´ moves at speed v in the negative z-direction with respect to inertial observer O.
Write down the relationship between the sets of coordinates used by the two different observers.

A.2 A rocket moves at speed 4c/5 towards the earth. It fires a missile at a speed of 3c/5 opposite to
its direction of motion as measured on the rocket. With what speed does the missile strike the earth?

A.3 If A = (&#955;, 1,2,2) is a future-pointing timelike 4-vector, what is the maximum information you know about &#955;.

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##### Solution Summary

This solution is comprised of a detailed explanations of the problems of the special theory of relativity.
It contains step-by-step explanation for the following problems:
A.1 Inertial observer O´ moves at speed v in the negative z-direction with respect to inertial observer O.
Write down the relationship between the sets of coordinates used by the two different observers.

A.2 A rocket moves at speed 4c/5 towards the earth. It fires a missile at a speed of 3c/5 opposite to
its direction of motion as measured on the rocket. With what speed does the missile strike the earth?

A.3 If A = (&#955;, 1,2,2) is a future-pointing timelike 4-vector, what is the maximum information you know about &#955;.

Solution contains detailed step-by-step explanation.

##### Solution Preview

A 1 :- Let the two observers O and O′ are observing the same event at any point P whose co-ordinates are
(x,y,z,t) and (x′,y′,z′,t′) in two inertial frames of reference S and S′ respectively.
Since the inertial observer O′ moves at speed v in the negative z-direction with respect to
inertial observer O, the relationship between the two sets of co-ordinates used are
x′ = x, y′ = y , z′ = β(z + vt) , t′ = β(t + vx/c2) where β = 1/[1 - ...

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• BSc, Manipur University
• MSc, Kanpur University
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