Question

A group of rowdy teenagers near a wind turbine decide to place a pair of

pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.

a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.

b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.

Answer 1

a) Sinusoidal functions are y = a sin [b(x-h)] + k (or)

y = a cos [b(x-h)] + k

Where a is amplitude a= (max-min)/2=(16-2)/2=7

period p= 2π/b

b=2π/30

Horizontal transformation to 10 units right h=10

k= (max+min)/2=(16+2)/2=9

h = 7 cos [π/15(t-10)]+ 9

b) t=10min=600 sec

substitue in the above equation

h=5.5m