unting Supersonic Uy = 500 mis plane V8-1000-k 옷 You Example A supersonic plane moves away from you along the x axis with speed 1000 m/s (about 3 times the speed of sound) relative to you. Another plane moves along the x axis away from you and away from the second plane at speed 500 m/s rel- ative to the first plane. How fast is the second plane moving relative to you? TII Another plane 2. Calculate the correction term in the denomina- tor of Equation 39-18a: Picture the Problem These speeds are so small compared with c that we expect the classical equations for combining velocities to be accurate. We show this by calculating the correction term in the denominator of Equation 39-18a. Let frame S be your rest frame and frame S' be moving with velocity V 1000 m/s. The first plane is then at rest in frame S' and the second has velocity u = 500 m/s in S'.. = 1. The classical formula for combining velocities, u + V = 500 m/s gives for the velocity of the second plane rela- tive to you: +1000mls <= 1500 m/s ***** Игров 1-4x470 TER 570 = 500-(-1000) P.5 Vu (1000) (500) (3 x 108)² 25.6 x 10 1500 m/S t Remark This correction term is so small that the classical and relativistic re sults are essentially the same. Mare -12 = 500+1000 LO v=-1000 m Ux=+500 mls (away from you) 5

unting Supersonic Uy = 500 mis plane V8-1000-k 옷 You Example A supersonic plane moves away from you along the x axis with speed 1000 m/s (about 3 times the speed of sound) relative to you. Another plane moves along the x axis away from you and away from the second plane at speed 500 m/s rel- ative to the first plane. How fast is the second plane moving relative to you? TII Another plane 2. Calculate the correction term in the denomina- tor of Equation 39-18a: Picture the Problem These speeds are so small compared with c that we expect the classical equations for combining velocities to be accurate. We show this by calculating the correction term in the denominator of Equation 39-18a. Let frame S be your rest frame and frame S' be moving with velocity V 1000 m/s. The first plane is then at rest in frame S' and the second has velocity u = 500 m/s in S'.. = 1. The classical formula for combining velocities, u + V = 500 m/s gives for the velocity of the second plane rela- tive to you: +1000mls <= 1500 m/s ***** Игров 1-4x470 TER 570 = 500-(-1000) P.5 Vu (1000) (500) (3 x 108)² 25.6 x 10 1500 m/S t Remark This correction term is so small that the classical and relativistic re sults are essentially the same. Mare -12 = 500+1000 LO v=-1000 m Ux=+500 mls (away from you) 5

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