High School Pre-Cal

Question

A bicycle wheel is 27 inches in diameter. If the wheel is turning at
10 rotations per minute and point P touches the ground at t = 0 seconds, how far above the ground will point P be at t = 7 seconds?



A.6.25 inches
B.6.75 inches
C.7.25 inches
D.7.75 inches

Answer 1

C=3.14*27

C=84.8313 in

10 revs per minute

84.8313/60=14.138 in in 1 sec

in 7 sec, 7*14.138=98.966 in

98.966-84.831=14.135 in more than 1 revolution

the arc is 14.135 in starting from the very bottom and ending on the left side before the quarter clockwise turn

the left endpoint of this arc is how far above the ground ?

draw a circle with a vertical and horizontal diameter

draw the radius to the left endpoint; the radius to the endpoint on the ground is part of the vertical diameter

draw a horizontal line from the left endpoint of the arc to the vertical radius; this forms a right triangle

find the central angle of the arc which is 14.135 in, call it x

arc length is equal to (x/360)(2)(pi)(r)

substitute

14.135=(x/360)(2)(3.14159)(13.5)

14.135=(x/360)(84.8229)

14.135=x/4.244137

x=04.244137*14.135

x=59.99º or about 60º

therefore the other acute angle is about 30º

the side opposite the 30º angle is half of the hypotenuse 

half the hypotenuse is 6.75 in (half of the radius; the diameter is 27 in so the radius is 13.5 in)

the opposite side is the same height

the opposite side is the distance from the left endpoint of the arc to the ground

therefore, the point P will be 6.75 in above the ground in 7 seconds