Question

Whitney starts the engine on her small private airplane. The engine drives a propeller with a radius of 6.5 feet and its centerline 10.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 850 revolutions per minute. The height of one propeller tip as a function of time is given by h = 10.5 + 6.5 sin(850t), where h is the height in feet and t is the time in minutes. Find h when t = 2 minutes.

a.
4.1 ft
b.
9.4 ft
c.
16.9 ft
d.
11.6 ft

Answer 1

4.1 ft

Explanation:

All we need to do is substitute "t" as 2 minutes to determine the height:

h = 10.6 + 6.5 sin(850*2),

Remove full rotations of 360 until the angle is between 0 and 360° :

h = 10.6 + 6.5 sin(1700) = 10.6 + 6.5 sin(260)

Now evaluate sin(260) :

h = 10.6 - 6.40125... = 4.1987496

Your solution should be 4.1 ft (though it actually should be 4.2 ft)