1. A 1000m long and 200m wide (when at rest) spaceship equipped with a chronometer is sent on a roundtrip to their Galactic Base, 8 light years away. (a) Astronauts start the trip after celebrating their captains 29th birthday and they want to make a round trip and return to Earth on the eve of the captains 30th birthday. The ship travels with a constant velocity. Calculate the required speed of the spaceship. (b) According to the clocks on Earth, how long does this trip take? (c) At which speed the age difference between the captain of the spaceship and her twin sister staying on Earth will be minimal when the spaceship returns to Earth? (d) How large is the distance from Earth to Galactic Base from the ships point of view (when the ship is at the beginning of its journey but its speed is already equals the minimum speed calculated above)? (e) Calculate the proper length of the ship when the speed of the ship is 0.5 c relative to Earth. (f) Calculate the length and the width of the ship in a reference frame where the velocity of the ship is directed from its tail to head and the speed is 0.5 c. 2. When travelling in space, a ship (length 1000m in its rest frame) passes an identical ship, which is at rest relative to Earth. The captain of the moving ship decides to measure the speed of her ship. She looks out of a window and uses her clock to measure the time between the moments when the head and the tail of the other ship pass. The result of the measurement is 1 ìs. Calculate the speed of the “moving” ship relative to Earth. 3. Two ships start simultaneously from Earth and move in directions, which are orthogonal to each other and with equal velocities of 0.8 c. Calculate the distance between the ships as function of time in the rest frame of one of the ships. 4. Two ships are moving toward each other with velocity of 0.7 c. At time zero in reference frame (reference frame of Earth), Ship 1 nearly collides with Earth and Ship 2 is at the distance of 105 km from Earth. (a)How long does it take according to the clock on Earth before the ships collide? What are the coordinates of each ship at the collision? (b)The clock in reference frame where Ship 1 is always at origin and at rest is set to zero when Ship 1 nearly collides with Earth. What will the clock in show when the two ships collide? (c)Calculate the distance between the two ships in when the Ship nearly collides with Earth. (d)The distance to the other ship divided by the time until the collision (all measured in the reference frame of Ship 1) gives the relative velocity of the two ships. Calculate the relative velocity and comment on the value.