Question

Samir watches a 100-minute movie on his spaceship. Maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be?according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

Answer 1

1. 50 m

2. The time it would take Maria to reach planet x according to Samir is 0 years

Step-by-step explanation:

1. Here we have;

`\sqrt{1 - (v^(2))/(c^(2))} = (T_(0))/(T) = (l)/(l_(0))`

Where:

v = Velocity of Maria's spaceship relative to Samir's spaceship

c = Speed of light

T₀ = Time measured on Samir's spaceship = 100 minutes

T = Time observed on Maria's spaceship = 125 minutes

l = Length of Samir's spaceship as observed by Maria = 40 m

l₀ = Original length of Samir's spaceship = Required

Plugging the values, we have;

`(100)/(125) = (40)/(l_(0))`

l₀ = 125/100 × 40 = 1.25 × 40 = 50 m

Samir observes his own spaceship to be 50 m

2. Whereby the speed of Maria = 0.5·c

Therefore;

`\sqrt{1 - ((0.5c)^(2))/(c^(2))} = (T_(0))/(9)`

T₀ = 9 × √0.75 = 7.79 years is the estimated time a stationery observer sees Mari reach planet x

For Samir, we have;

Speed of Maria relative to Samir = 0.5·c - (-0.5·c) = c

Therefore;

`\sqrt{1 - (c^(2))/(c^(2))} = (l)/(l_(0)) =0`

Which gives, l = l₀ = 0

Hence, since to Samir, the distance from Maria's is spaceship to planet x = 0, then the time it would take Maria to reach planet x according to Samir = 0 years.