a small windmill has it's centre 6m above the ground and blades 2m in length. a point P at the tip of one blade makes a complete rotation in 12 seconds.

Question

a) determine a function that gives the height of point P above the ground at time t.

b) what is the height at point P at 5 seconds?

c) at what time during the first cycle is point P exactly 7m above the ground?

Answer 1

(h(t)=2cos(2πt/12)+6 , t in seconds, when t=0, h=8, when t=6, h=4

when t=5, h=2cos(5π/6)+6=4.27 meters at t=5 given starting point is 8

when h=7, πt/6=cos^-1.5

t=(π/3)/(π/6)=2