Team **Space Chemistry** has summarized 10 examples of **Lorentz Transformation question** problems and their solutions for 12th grade high school students from various book publishers. In helping the quality of education in Indonesia, we always contribute so that students can learn and understand the calculation of questions related to the material from the Lorents transformation (Part of Special Theory of Relativity).

## 1 – 10 Lorentz Transformation Problems and Their Discussion

1. According to O’ a flash of light strikes at x’ = 60 m, y’ = z’ = 0, t’ = 8 x 10‾^{8} O’ has a velocity of 0.6 c along x from O. Find the spacetime coordinates of the lightning strike according to O ?

#### Discussion:

2. A light is switched on at point x = 160 km at t = 4 x 10‾^{4} s when observed by O. From this event, when viewed by O’, it has a velocity of 0.6 c. How long does the flash of light travel relative to O ?

#### Solution:

3. Evaluate

(a) v = 10‾² c

(b) v = 0.9998 c !

#### Solution:

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4. Observer O finds that two events are separated in space by a distance of 200 m and in time 4 x 10‾^{6} How fast must an observer O’ have to move relative to O for the two events to be simultaneous for O’ ?

#### Solution:

5. A train ½ mile long (measured by an observer inside the train) travels at 100 miles/hour.

Two flashes of light hit the ends of the train simultaneously as seen from the side of an observer on earth. What is the time difference measured by the observer in the train?

#### Solution:

6. Observer O’ has a speed of 0.6 c relative to O and his time is adjusted so that t = t’ = 0 when x = x’ = 0. If O observes that the flash fires at point x = 100 m and at t = 24 x 10‾^{6} s, what is the time for this occurrence when viewed by observer O’ ?

#### Solution:

7. The space-time coordinates for the two events measured by observer O are x_{1} = 4 x 10^{4} m, y_{1} = z_{1} = 0 m, t_{1}‘ = 4 x 10^{-4} s and x_{2} = 14 x 10^{4} m, y_{2} = z_{2} = 0 m, t_{2} = 2 x 10^{-4} v/c = -½. What is the difference between the two events from O”s point of view?

#### Solution:

#### Also Read: 10+ Special Relativity Questions and Answers [+Pembahasan]

8. When observed by O a flash of light strikes a point x = 60 m, y = z = 0 m and at t = 18 x 10‾^{8} Observer O’ has a speed of 0.6 c. How does t’ look to the second observer O’ ?

#### Solution:

9. A flashlight is lit at point x = 100 km at t = 2 x 10‾² s when observed by O. From this event, viewed by O’, it has a speed of 0.8 c. How long does the flash of light travel relative to O ?

#### Solution:

10. Derive the time expansion formula using the Lorentz transformation. Consider a bell at a point in the moving frame. When the observer is at point S it will get the time based on the equation.

#### Solution:

Time dilation with Lorentz transform: