A roller coaster is on a flat track heading towards an incline, moving at 5.90 m/s. After it has gone down the 78.0° incline (measured from the horizontal), the roller coaster is now going at a speed of 35.0 m/s. What is the length of the incline?
gravitational force down incline = m g sin 78
so
acceleration down incline = a = g sin 78 = 9.81 * sin 78 = 9.60 m/s^2
v = Vi + a t
35 = 5.9 + 9.6 t
t = 3.03 s
speed is linear with time so use average speed
= (5.90 + 35.0)/2 = 20.45 m/s
d = speed * time = 20.45 * 3.03 = 62 meters