Answer :
Answer:
1. 50 m
2. The time it would take Maria to reach planet x according to Samir is 0 years
Explanation:
1. Here we have;
[tex]\sqrt{1 - \frac{v^{2}}{c^{2}}} = \frac{T_{0}}{T} = \frac{l}{l_{0}}[/tex]
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;
[tex]\frac{100}{125} = \frac{40}{l_{0}}[/tex]
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;
[tex]\sqrt{1 - \frac{(0.5c)^{2}}{c^{2}}} = \frac{T_{0}}{9}[/tex]
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;
[tex]\sqrt{1 - \frac{c^{2}}{c^{2}}} = \frac{l}{l_{0}} =0[/tex]
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.
