Introduction to modern physics (phy 360) due: 09/07/2018 problem 1. previously we showed that the form of the wave equation changes in the galilean transformations. in this exercise use the lorentz transformation for conneeting two inertial frames with relative velocities of v and show that argue why this result implies that the speed of light is the same in both frames problem 2. bob is speeding away from alice with the constant speed of 0.8e towards east meanwhile alice notices that a satellite is moving towards her with the speed of 0.6c. what is the speed of the satellite in bob's frame if the satellite is moving towards alice from (a) mest (b) south? problem 3. a rod lies parallel to the x-axis of reference frame s, moving along this at a speed of 0.8c. its rest length is 1.0 m. what will its measured length be in frame s? problem 4. a rod is placed such that it is making a 45 degre angle with the x-axis in framae s. an observer in a moving frame s measures the angle between the rod and the x-axis to be 80 the frame s? degrees. what is the relative velocity the frane s' with respect to problem from the book : 1-20, 1-21, 1-24, 1-27

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b