An amusement park roller coaster starts out on a level track 50.0 m long and then goes down a 50.0-meter incline at an angle of 30° to the vertical. It then goes up a 20.0-meter ramp with an incline of 20° to the horizontal.
(a) What is the magnitude and direction of the displacement vector from the initial location to the bottom of the 20.0-meter ramp?
(b) If it takes 20.0 s to go from the initial location to the bottom of the 20.0-meter ramp, what is the average velocity dur-ing that time? After the 20.0-meter ramp the coaster travels 15.0 m on flat ground then enters, from the bottom, the inside of a circular track of radius r. After subtending (traveling) 25.0 º around and up the circular track it is noticed that the coaster is half way up to its original height
in reference to its lowest position.
(c) What is the radius of the circular track?
Extra-credit: if the initial speed of the coaster is 5 m/s how long does it take to reach the bottom of the circular track?