Question

Big Ben is the largest clock tower in England and overlooks the Houses of Parliament and the Thames River. The minute hand of the clock measures 36 feet in length. How far does the tip of the minute hand move in 20 minutes

Answer 1

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