Two jets are flying with velocities 2000/& 1000km/h towards each other . Applying Einstein relativity formula find relative velocity of jets
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Two rockets of rest length L0 are approaching the earth from opposite directions at velocities ±c/2. How long does one of them appear to the other?
Answer: Let’s pick one rocket (call it rocket 1) and consider how fast the other rocket (rocket 2) looks in this frame. In the Earth frame, rocket 1 has velocity c/2 and rocket 2 has velocity −c/2. Applying the velocity addition law gives
′ v2 − v1
v2 = 2 =
(−c/2) − (c/2) 1 − (c/2)(−c/2)/c
4
2 = − c,
1 − v1v2/c
i.e., rocket 2 looks like it is approaching at 54 c. Applying the Lorentz contraction formula gives
2 ′L0 43
5
L==L01− =L0. γ55
Answer: Let’s pick one rocket (call it rocket 1) and consider how fast the other rocket (rocket 2) looks in this frame. In the Earth frame, rocket 1 has velocity c/2 and rocket 2 has velocity −c/2. Applying the velocity addition law gives
′ v2 − v1
v2 = 2 =
(−c/2) − (c/2) 1 − (c/2)(−c/2)/c
4
2 = − c,
1 − v1v2/c
i.e., rocket 2 looks like it is approaching at 54 c. Applying the Lorentz contraction formula gives
2 ′L0 43
5
L==L01− =L0. γ55
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