Express the unit vectors in spherical polar coordinate systems in terms of the cartesian unit vectors ii) using the results of i), find the time derivatives of iii) using the above results, find an expression for the velocity vector in terms of iv) derive the expression for speed using the velocity vector from iii).

Atrain is traveling at 30.0 m/s relative to the ground in still air. the frequency of the note emitted by the train whistle is 262 hz. the speed of sound in air should be taken as 344 m/s. what frequency (f approach) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it? what frequency (f recede) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?