7. At the bottom of its rotation, the tip of the blade on a windmill is 5 m above the ground. At the top of its rotation, the blade tip is 19 m above the ground. The blade rotates once every 10 seconds. An insect lands on the tip of the blade when it is at its highest point 4 seconds after you start observing the windmill.

Question

b. State an equation that represents the height of the windmill blade.

Answer 1

Let h(t) represent the height of the windmill blade at time t seconds after the windmill starts rotating.

The height of the blade tip can be modeled by a sinusoidal function, since the blade completes one full rotation every 10 seconds.

At the lowest point (t=0), the height is 5m, and at the highest point (t=5), the height is 19m.

Therefore, the equation that represents the height of the windmill blade is:
h(t) = -7cos[(π/5)t] + 12