A spacecraft approaching the earth launches an exploration vehicle. After the launch, an observer on earth sees the spacecraft approaching at a speed of 0.74c and the exploration vehicle approaching at a speed of 0.98c. What is the speed of the exploration vehicle relative to the spaceship?
I keep getting .259 which is the wrong answer. I don't know what Im doing wrong I use the velocity addition formula but it never works. Please help!!
0.98c is the relative velocity of the probe with respect to the Earth (V3). That is the relativistic sum of the probe velocity (V2) with respect to the spaceship, and the spaceship with respect to Earth (V1).
V3 = (V1 + V2)/[1 + (V1*V2)/c^2]
You want to solve for V2.
I get V2 = 0.873c
Thank you. i sort of had to back track to get the answer you got but eventually got it. Thank you!!
To solve this problem, you can use the relativistic velocity addition formula. However, it seems there might be a mistake in your calculation. Let's go through the correct steps to find the speed of the exploration vehicle relative to the spaceship.
The relativistic velocity addition formula states that the velocity of an object moving at a speed v1 relative to an observer, as observed by another observer moving at a speed v2 relative to the same object, can be found using the formula:
v = (v1 + v2) / (1 + (v1 * v2) / c^2)
Where:
- v is the relative velocity (the velocity observed by the second observer)
- v1 is the velocity of the object relative to the first observer
- v2 is the velocity of the first observer relative to the second observer
- c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)
In this scenario:
- The velocity of the spacecraft relative to the earth observer (v1) is 0.74c
- The velocity of the exploration vehicle relative to the earth observer (v2) is 0.98c
Let's substitute these values into the formula and calculate the relative velocity:
v = (0.74c + 0.98c) / (1 + (0.74c * 0.98c) / c^2)
v = (1.72c) / (1 + (0.7252c^2) / c^2)
v = (1.72c) / (1 + 0.7252)
v = (1.72c) / 1.7252
v ≈ 0.997c
Therefore, the speed of the exploration vehicle relative to the spaceship is approximately 0.997 times the speed of light. Hence, the exploration vehicle is moving very close to the speed of light relative to the spaceship.