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In this lesson, we will learn how to calculate the change in the observed length as measured by an observer moving with a relative velocity.

Q1:

A spaceship that has a proper length of 2 . 0 0 Γ 1 0 2 m, moves at 0 . 9 7 0 π relative to the Earth. What is the spaceshipβs length as measured by an observer on the Earth?

Q2:

A spaceship (A) is moving at speed π / 2 with respect to another spaceship (B). Observers in A and B set their clocks so that the event at ( π₯ , π¦ , π§ , π‘ ) of turning on a laser in spaceship B has coordinates (0, 0, 0, 0) in A and also (0, 0, 0, 0) in B. A photon from the laser in spaceship B arrives at ( π₯ = 1 . 0 0 , 0 , 0 ) m at π‘ = 0 in the frame of ship A.

What will be the time value π‘ β² at which the observer in spaceship B measures the photonβs arrival?

What displacement value π₯ β² will the observer in spaceship B measure for the position of the arriving photon?

Q3:

How fast should an athlete run for them to perceive a 200 m race as a 200 yd race given that 1 yd = 0.9144 m?

Q4:

An observer located at the origin of an inertial frame π sees the flash of a flashbulb occur at the position π₯ = 1 5 0 k m and at the time π‘ = 4 . 5 0 Γ 1 0 ο± οͺ s . The system π ο is moving along the π₯ -direction of π at a velocity of 0 . 6 0 0 π .

At what time in the π ο system did the flash occur?

At what π₯ -position did the flash occur as measured in the π ο system?

Q5:

An astronaut measures the length of his spaceship to be 100 m, while an observer on Earth measures it to be 25.0 m.

Find the Lorentz factor πΎ that relates the values of measurements by the astronaut and the observer on Earth.

What is the velocity of the spaceship relative to earth?

Q6:

Spaceship A is moving at speed π 3 with respect to another spaceship B. A rod of length 2 m is laid out on the π₯ -axis in the reference frame of B from the origin to (2.00, 0.00, 0.00). What is the length of the rod as measured by an observer in the reference frame of spaceship A? Give your answer to 3 significant figures.

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