Recitation 1-3 (1)

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University of Texas *

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Mechanical Engineering

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Jan 9, 2024

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Recitation 1: (September 1, 2023) Problem 1: a) A passenger in a train moving at 30 m / s passes a man standing in a station platform at t = t ' = 0 . Twenty seconds after the train passes him, the man on the platform determines that a bird flying along the tracks in the same direction as the train is 800 m away. What are the coordinates of the bird as determined by the passenger? b) Five seconds after making the first coordinate measurement, the man on the platform determines that the bird is 850 m away. Find the (constant) velocity of the bird as determined by the man on the platform and by the passenger on the train.
Problem 2: A sample of radioactive material, at rest in the laboratory, ejects two electrons in opposite directions. One of the electrons has a speed of 0.6 c and the other has a speed of 0.7 c , as measured by the laboratory observer. According to classical velocity transformations, what will be the speed of one electron as measured from the other? Problem 3: A train with a velocity of 60 mi / hr passes through a railroad station at 12:00. Twenty seconds later a bolt of lightning strikes the railroad tracks one mile from the station in the same direction that the train is moving. Find the coordinates of the lightning flash as measured by an observer at the station and by the engineer of the train. Problem 4: A hunter on the ground fires a bullet in the northeast direction which strikes a deer 0.25 miles from the hunter. The bullet traves at a speed of 1800 mi / hr . At the instant when the bullet is fired, an airplane is directly over the hunter at an altitude h of one mile and is traveling due east with a velocity of 600 mi / hr . When the bullet strikes the deer, what are the coordinates as determined by an observer in the airplane?
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