Question

. two planets are on a collision course, heading directly toward each other at 0.250c. a spaceship sent from one planet approaches the second at 0.750c as seen by the second planet. what is the velocity of the ship relative to the first planet?

Answer 1

the velocity of the spaceship relative to the first planet is approximately 299,792,457.7 meters per second.

Step-by-step explanation:

To determine the velocity of the spaceship relative to the first planet, we can use the relativistic velocity addition formula. The formula is as follows:

v' = (v1 + v2) / (1 + (v1*v2) / c^2)

Where:

v' is the relative velocity between the two planets

v1 is the velocity of the spaceship as observed by the first planet (0.750c)

v2 is the velocity of the two planets approaching each other (0.250c)

c is the speed of light in a vacuum

Plugging in the given values, we can calculate the relative velocity:

v' = (0.750c + 0.250c) / (1 + (0.750c * 0.250c) / c^2)

= (1.000c) / (1 + (0.1875) / c^2)

Since c represents the speed of light, which is approximately 299,792,458 meters per second, we can substitute it into the equation:

v' = (1.000 * 299,792,458 m/s) / (1 + (0.1875) / (299,792,458 m/s)^2)

≈ 299,792,458 m/s / (1 + 5.917 * 10^(-10))

≈ 299,792,458 m/s / (1.0000000005917)

Thus, the velocity of the spaceship relative to the first planet is approximately 299,792,457.7 meters per second.