Problem 1: The ionosphere is a region of electrically neutral gas, composed of positively charged ions and negatively charged electrons surrounding the earth at approximately 200km in the upper atmosphere. If a radio wave passes through the ionosphere, it causes the charges particles to accelerate. The position of an electron in the upper atmosphere in presence of the radio wave can be given as (by choosing the axis appropriately such that it becomes a one-dimensional problem) x(t) = (eE/m) sin(ot) where e is the charge of the electron, E is a constant and m is its mass, and @ is the frequency of the radio wave. Assume that the electron is initially at rest. a) Sketch the motion of the electron on a position-time graph. b) Calculate the velocity of the electron as a function of time and write an expression for the maximum value that this velocity can have. In terms of e, E, m and w, at what time t does the electron have maximum velocity? c) Calculate the expression for the acceleration of the electron as a function of time. d) What is the acceleration of the electron when the velocity is at its maximum? e) Could we use the kinematic formulae we have studied to describe the motion of the electron? Explain