What is the Speed of Ship A as Observed from Ship B?

In summary, the conversation discussed two spaceships approaching Earth from opposite directions, with ship A moving at a speed of 0.753c and ship B at a speed of 0.851c as observed by an observer on Earth. The question asked for the speed of ship A as observed from ship B, and the speed of ship B as observed from ship A. The equation v = (v' + u) / (1+ (v'u)/(c^2)) was used to calculate the speeds, and after plugging in the values, a negative was needed to obtain the correct answer.
  • #1
Oijl
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Homework Statement


Nevermind, got it.
Two spaceships approach the Earth from opposite directions. According to an observer on the Earth, ship A is moving at a speed of 0.753c and ship B at a speed of 0.851c. What is the speed of ship A as observed from ship B? Of ship B as observed from ship A?

Homework Equations


v = (v' + u) / (1+ (v'u)/(c^2))
and so
v' = (u - v) / ((vu)/(c^2) - 1)

The Attempt at a Solution


u is the speed of A as observed from Earth.
v is the speed of B as observed from Earth.
v', then, would be the speed of A or B as observed from the other ship.

The values 0.753c and 0.851c plugged in, I get 0.2728c = v'.

The speed of one ship as observed by the other ship should be greater than either of the ship's speeds as observed on earth. So where am I incorrect?
 
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  • #2
Nevermind, got it just after I posted. I needed a negative! Always a negative.
 

FAQ: What is the Speed of Ship A as Observed from Ship B?

What is relativistic velocity addition?

Relativistic velocity addition is a mathematical formula used in special relativity to calculate the velocity of an object as observed by two different observers who are in relative motion to each other.

How is relativistic velocity addition different from classical velocity addition?

Relativistic velocity addition takes into account the effects of time dilation and length contraction, which occur at high velocities and are predicted by Einstein's theory of special relativity. Classical velocity addition, on the other hand, assumes that time and space are absolute and do not change with velocity.

What is the formula for relativistic velocity addition?

The formula for relativistic velocity addition is V = (u + v) / (1 + (uv/c^2)), where V is the observed velocity, u is the velocity of the object as observed by one observer, v is the velocity of the observer relative to the object, and c is the speed of light.

Can the velocity of an object exceed the speed of light when using relativistic velocity addition?

No, according to Einstein's theory of special relativity, the speed of light is the maximum speed at which any object can travel. Therefore, the resulting velocity calculated using relativistic velocity addition cannot exceed the speed of light.

Why is relativistic velocity addition important in physics?

Relativistic velocity addition is important because it allows us to accurately calculate the observed velocity of objects at high speeds. It is a fundamental concept in special relativity and has implications for many other theories and phenomena, such as time dilation and the twin paradox.

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