# 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 = (λ, 1,2,2) is a future-pointing timelike 4-vector, what is the maximum information you know about λ.

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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 = (λ, 1,2,2) is a future-pointing timelike 4-vector, what is the maximum information you know about λ.

Solution contains detailed step-by-step explanation.

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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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