A spaceship is moving to the right at speed 0.95c. A banner of length 2m and the width of 1.5m with respect to the passengers on the spaceship is hung out the bottom of the spaceship for the physicsts in the Earth-based observatory to track. (a) What is the length of the banner the physicists will measure. Because the width of the banner is quite long, it takes some time to roll up. If the passengers on the spaceship note that it takes 300s to roll the banner back inside the spaceship. (b) How long will the physicists measure. If a secondary spaceship is launched to travel to the right at speeds 0.8c with respect to the first spaceship, what is the secondary spaceship's speed with respect to earth?
A spaceship is moving to the right at speed 0.95c. A banner of length 2m and the width of 1.5m with respect to the passengers on the spaceship is hung out the bottom of the spaceship for the physicsts in the Earth-based observatory to track.
(a) What is the length of the banner the physicists will measure. Because the width of the banner is quite long, it takes some time to roll up. If the passengers on the spaceship note that it takes 300s to roll the banner back inside the spaceship.
(b) How long will the physicists measure. If a secondary spaceship is launched to travel to the right at speeds 0.8c with respect to the first spaceship, what is the secondary spaceship's speed with respect to earth?
(a)
Let l0 and l denote the banner’s length in the spaceship’s frame and in the rest Earth frame, respectively.
Since the banner itself is in the spaceship’s frame, the spaceship observers note the banner’s actual length.
Let v1 denote the first spaceship’s speed with respect to the Earth. Earth moves with v1 in the opposite direction with respect to the spaceship’s frame.
As a result, the Earth observers note the banner’s contracted length (l), which can be evaluated by using the Lorentz length-contraction formula as follows:
(b)
Let t0 and t denote the time taken in the spaceship’s frame and in the rest Earth frame, respectively, to roll up the banner.
Since the banner itself is in the spaceship’s frame, the spaceship observers note the actual time.
The Earth observers note the dilated time (t), which can be evaluated by using the Lorentz time-dilation formula as follows:
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