Answer:
75.408 ft
Step-by-step explanation:
In 20 minutes, the angle swept by a minute hand is calculated as
(20/60) x 360° = 120°
The length of the minute hand = 36 ft
To calculate the distance moved by the minute hand, we solve for the fraction of the circumference of a circle swept by the minute hand in going through this 20 min.
we use the expression
Distance moved by the tip of the minute hand d = (θ/360) x 2πR
where
θ is the angle swept in the 20 minutes = 120°
R is the length of the minute hand, which is the radius of the circle formed if the minute hand moves completely in a 360° motion round the clock.
R = 36 ft
substituting values, we have
d = (120/360) x (2 x 3.142 x 36) = 75.408 ft
The tip of the minute hand moves 0.21 ft in 20 minutes.
The minute hand sweeps an arc of length L given by
L = Ф/360° × 2πR where
So, substituting the values of the variables into the equation, we have
L = Ф/360° × 2πR
L = 1/3°/360° × 2π × 36 ft
L = 1/(3 × 360) × 2π × 36 ft
L = 1/(3 × 10) × 2π ft
L = 1/30 × 2π ft
L = 1/15 × π ft
L = 3.1416/15 ft
L = 0.2094 ft
L ≅ 0.21 ft
So, the tip of the minute hand moves 0.21 ft in 20 minutes.
Learn more about length of an arc here:
https://brainly.com/question/8402454
