Sam is on Earth and sees two spaceships. Alpha and Beta, at a distance 30,000,00

Question

Sam is on Earth and sees two spaceships. Alpha and Beta, at a distance 30,000,000 km from each other. The spaceships are out of control and are headed to a head-on collision. Sam measures spaceship Alpha to be moving with a speed of 0.6c and spaceship Beta with a speed 0.8c. How long will it be, from Sam's point of view, before the two spaceships collide? How much time do the passengers of Alpha have to evacuate before the spaceships collide? How fast is spaceship Beta traveling from the point of view of Alpha? Alpha sends a light signal to Beta to warn the passengers of that ship. Alpha uses a red laser (wavelength = 600 nm). Can the passengers on Beta see the signal? From Sam's point of view, both spaceships are identical. Is Alpha or Beta longer when measured by their respective passengers?

Explanation / Answer

a)

since sam is at rest , the distance between two spaceships = 3 x 1010 m

b)

actual time = T = 3 x 1010 / (0.8c + 0.6c) = 3 x 1010 / (1.4 x 3 x 108) = 71.43 sec

for alpha spaceship :

V = 0.6 c

T' = T/sqrt(1 - V2/c2) = 71.43 / sqrt(1 - (0.6)2) = 89.3 sec

c)

relative velocity = (0.8 c + 0.6 c) / (1 + (0.8) (0.6)) = 0.95 c

e)

according to their respective passenger , the length of each spaceship will be smaller

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