The height above the surface of the water, h, in centimeters, of a certain spot on a paddle of a miniature river boat is modeled by h(t) = 5.5cos(72t) +35

Question

where t is the time in second since the boat started moving. 

 

A) What are the maximum and minimum height of the spot on the paddle? 

B) What is the speed of the rotation? 

C) How long does it take for the wheel to make 6 revolutions? 

 

I'm unsure how to find this stuff based on the question. It's grade 11 trig. Thanks in advance for your help! 

Answer 1

Note that 72 = 11.459156*2*pi with period 0.087266463 sec. The max height is 5.5+35 at t=0,0.087266463*n, n=0,1,2 ... , The minimum height is 29.5 at t = pi/72 = 0.043633 sec or n*pi/72*n, n=1,2,3 ... .The speed of rotation is the reciprocial of thetime for one cycle or  72/(2*pi) = 11.4548 cycles/sec. It takes 6*pi/72 or 0.2618 sec for 6 revolutions.