The minute hand of a clock is 6 inches long and moves from 3 o clock to 5 o clock. how far does the tip of the minute hand move. Express your answer round to two decimal places. Can you solve this?
Each hour is equal to 30° or π/6 radians
So to go from 3:00 to 5:00 would take 2π/6 or π/3
the arclength = rØ
= 6(π/3) or 2π inches
= appr 6.28 inches
or
circumference = 2π(6) = 12π
the time from 3:00 to 5:00 represents 1/6 of a rotation = (1/6)(2π) = 2π = appr 6.28 inches as above
Yes, I can help you solve this problem.
To find how far the tip of the minute hand moves, we can first calculate the circumference of the clock. The minute hand is essentially tracing out a circle as it moves from 3 o'clock to 5 o'clock.
The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the minute hand is 6 inches long, which means the radius of the circle is half of that length, or 3 inches.
Plugging in the values, we can calculate the circumference of the clock:
C = 2π(3) = 6π
Now, to find how far the tip of the minute hand moves from 3 o'clock to 5 o'clock, we need to determine the angle it covers.
Between each hour on a clock, there are 30 degrees (360 degrees divided by 12 hours). So, from 3 o'clock to 5 o'clock, the minute hand covers an angle of 2 hours * 30 degrees/hour = 60 degrees.
To find the distance traveled along the circumference, we can use the formula:
Distance = (angle/360) * Circumference
Plugging in the values, we have:
Distance = (60/360) * 6π ≈ 1.57 inches
Therefore, the tip of the minute hand moves approximately 1.57 inches.
So, the answer to your question is approximately 1.57 inches.