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.

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

,

where  

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So,  is the trajectory path equation to the circle

Let be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t  

At t= 10s, y = 16 m so we have,

---------------(1)

Also, at t= 25s, y =2 m so we have,

--------------(2)

Solving we have,

Therefore is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)