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A water wheel has a radius of 8m, however, 1m of it is submerged under water. the wheel rotates once every four minutes. if P is the point at the top of the wheel at time zero?

Answer 1

Asher Friedman

We'll do the equation first.

#P# is maximum at time zero, so this is a cosine.

# P (t)= A cos ( omega t ) - W #

Clearly #A# is the radius, # A=8# m. Once every four minutes means (for #t# in minutes)

#2 pi = omega (4)#

# omega = pi/2 #

#7 = P(0) = 8 cos( pi/2 (0) ) - W#

#W = 1#

#P(t) = 8 cos(pi/2 t) - 1#

We'll use the Socratic #cancel { text{crasher} } # grapher.

graph{8 cos(pi/2 x) - 1 [-.01, 4, -12, 12]}

# P(5) = 8 cos({5pi}/2) - 1 = 8 cos(pi/2)-1 = 8(sqrt{2}/2)-1= 4 sqrt{2} - 1 # meters

You'll have to do your own calculator; it's around #4.6 #m

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Answer from HIX Tutor

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