A variant on the carousel at a theme park is the swing ride. Swings are suspeneded from a rotating platform and move outward to form an angle x with the vertical as the ride rotates. The angle is related to the radial distance,r, in metres, from the centre of rotation; the acceleration, g=9.8 m/s^2 due to gravity; the speed,v, in metres per second, of the swing, accordon to the formula cotx=rg/v^2.

Question

a) Determine the angle x for a swing located 3.5 m from the centre of rotation and moving at 5.4 m/s, to the nearest hundredths of a radian.

Answer 1

well, just plug in the numbers:

cot x = (3.5)(9.8)/5.4^2

Answer 2

1.176