Respuesta :
In 1 hour, the hour hand sweeps across 1/12 of the clock's face. In 40 min, the hour hand travels (40 min)/(60 min) = 2/3 of the path it covers in an hour, so a total of 1/12 × 2/3 = 1/18 of the clock's face. This hand traces out a circle with radius 0.25 m, so in 40 min its tip traces out 1/18 of this circle's radius, or
1/18 × 2π (0.25 m) ≈ 0.087 m
The minute hand traverses (40 min)/(60 min) = 2/3 of the clock's face, so it traces out 2/3 of the circumference of a circle with radius 0.31 m:
2/3 × 2π (0.31 m) ≈ 1.3 m
The second hand completes 1 revolution each minute, so in 40 min it would fully trace the circumference of a circle with radius 0.34 m a total of 40 times, so it covers a distance of
40 × 2π (0.34 m) ≈ 85 m
The distances traveled by the tips of the hour hand, minute hand and second hand in a 40-min interval are 0.087 m, 1.3 m and 85 m respectively.
What are the hands of a clock?
In a clock, there are three hands of the clock. One is hour hand, second is minute hand and third one is second hand.
The hour hand of the clock is 0.25 m long. The hour hand sweep 1/12 of the clock face each hour (as there are 12 hours in a clock). Thus, in a 40-minute interval, it will travel the distance of,
[tex]d=2\pi\times\dfrac{40}{12\times60}(0.25)\\d\approx0.087\rm\; m[/tex]
The minute hand of the clock is 0.25 m long. In a 40-minute interval, it will travel the distance of,
[tex]d=2\pi\times\dfrac{40}{60}(0.31)\\d\approx1.3\rm\; m[/tex]
The second hand of the clock is 0.25 m long. In a 40-minute interval, it will travel the distance of,
[tex]d=2\pi\times\dfrac{40\times60}{60}(0.34)\\d\approx85\rm\; m[/tex]
Thus, the distances traveled by the tips of the hour hand, minute hand and second hand in a 40 min interval are 0.087 m, 1.3 m and 85 m respectively
Learn more about the hands of a clock here;
https://brainly.com/question/1138016
.
