46-48 Rate of rotation of the searchlight

Problem 46
A ship, moving at 8 mi/hr, sails east for 2 hr, then turns N 30° W. A searchlight, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hr after the start; (b) just after the turn.
 

Problem 47
In Problem 46, find when the light rotates most rapidly.
 

Problem 48
Prove that the result in Problem 46 and Problem 47 are independent of the speed of the ship.