An amusement park roller coaster starts out on a level track 50m long and then goes down a 50m incline at an angle of 30 degrees to the vertical(y-axis). It then goes up a 20m ramp with incline of 20degrees to the horizontal(x_axis), it then prceeds on a 15m horizontal track and enters, from the bottom, the inside of a circular track and after subtending 25degrees it noticed it is halfway up to its original height.
What is the radius of the circular track? If the initial speed is 5m/s how long does it take to reach the bottom of the circular track(end of 15m horizontal track).