The minute hand of a clock is 6 inches long. What distance does its tip move in 16 minutes?
the radian angle for 16 minutes
= (16/60)(2π) = 8π/15 radians
arclength = rØ
= 6(8π/15) = 16π/5 inches or 10.053 inches
or
one circumference = 2π(6) = 12π
so the fraction of rotation = 16/60
distance covered = (16/60)(12π = 16π/5
25.133
20
To find the distance that the tip of the minute hand moves in 16 minutes, we need to know how far it moves in one minute.
The minute hand of a clock moves in a circular motion, so we can use the formula for the circumference of a circle to determine the distance it travels:
Circumference = 2 * π * radius
In this case, the radius is the length of the minute hand, which is given as 6 inches.
Circumference = 2 * π * 6 inches
To find the distance the tip of the minute hand moves in one minute, we can divide the circumference by 60 (the number of minutes in an hour):
Distance in one minute = (2 * π * 6 inches) / 60 minutes = π / 5 inches
Therefore, the tip of the minute hand moves π / 5 inches in one minute.
To find the distance it moves in 16 minutes, we can multiply this value by 16:
Distance in 16 minutes = (π / 5 inches) * 16 minutes = 16π / 5 inches
So, the tip of the minute hand moves 16π / 5 inches in 16 minutes.