Mark Twain sat on the deck of a river steamboat. As the paddle wheel turned, a p

Question

Mark Twain sat on the deck of a river steamboat. As the paddle wheel turned, a point on the paddle blade moved in such a way that its distance, d, from the water's surface was a sinusoidal function of time. When his stopwatch read 4 seconds, the point was at its highest, 16 feet above the water's surface. The wheel's diameter was 18 feet, and it completed a revolution every 10 seconds. Write an equation for the function. How far above the surface was the point when Mark's stopwatch read 17 seconds? What is the first positive value of time at which the point was at the water's surface?

Explanation / Answer

Maximium point( 4,16) period = 10sec ;

Minimum point( 9, -2)

B = 2pi/10 = pi/5

a) Equation of function : f(t) = 9cos(pi/5(t -4) +7

b) t = 17sec ; f(17) = 9cos(pi/5( 17 -4) +7

= 9cos(13pi/5)

=4.21 feet

c) At 0.08 sec paddle point was coming out of water

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