A car travels due west along a straight road at a constant speed of 20m/s during a steady rainfall. The raindrops fall vertically downward at 8.0m/s relative to the ground. Neglect air resistance forces on the raindrops.
(a) Determine the angle that the streaks of rain make with the vertical as observed by the driver while the car moves at 20m/s.
(b) The car accelerates uniformly from 20m/s to 30m/s over a 5s interval. Assuming the vertical speed of the rain relative to the ground remains 8.0m/s, express the angle between the rain streaks and the vertical as a function of time during the acceleration period.
(c) Analyze the motion of the raindrops in a reference frame that initially moves with the car at 20m/s. In that frame, state the velocity components of the rain before the car accelerates and comment on how this frame choice affects the complexity of describing what the driver sees.
(d) Explain why adopting a moving frame aids intuition about the observed angle of the streaks yet does not alter the physical acceleration of the raindrops.