A town clock has an hour hand that is 60 cm long. How many cm does the tip of the hand move each second?
It takes the hour hand 12 hrs to go around the clock. This is equal to 12*3600 or 43200 seconds. Therefore, each second the hand moves 1/43200th of the way around a circle, or 2pi/43200 radians.
Using the equation x = r * theta, you can get x = 60 * 2 * pi / 43200, or 0.008727 cm.
Well, if the hour hand of the town clock is 60 cm long, it's definitely got some long 'arm' reach. Now, each hour on the clock is divided into 60 minutes, and each minute is divided into 60 seconds. So, let's do some math magic!
If the clock's hour hand covers a full 360-degree rotation in 12 hours, that means it moves at a speed of 30 degrees per hour. Since an hour has 60 minutes, it moves 0.5 degrees per minute, which is 0.008333 degrees per second.
Now, we also know that the circumference of a circle is 2πr, where 'r' is the radius of the circle. In our case, the radius is 60 cm. Thus, the circumference of the clock's movement is approximately 376.99 centimeters. So, if the hour hand completes a full rotation in 12 hours, it would cover 376.99 cm in 12 hours, or 31.4167 cm per hour.
Finally! There are 60 minutes in an hour, and 60 seconds in a minute. So, to find out how many centimeters the tip of the hand moves each second, we divide 31.4167 cm by 3600 (60 seconds multiplied by 60 minutes). And voila! The tip of the hand moves approximately 0.0087 centimeters each second.
To determine how many centimeters the tip of the hour hand moves each second, we need to know the time taken for the hour hand to complete one full rotation.
The hour hand completes one full rotation every 12 hours since there are 12 hours on a clock dial.
In 12 hours, there are 12 * 60 = 720 minutes.
In 720 minutes, there are 720 * 60 = 43,200 seconds.
So, it takes 43,200 seconds for the hour hand to complete one full rotation.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
For the hour hand, the radius (r) is given as 60 cm.
Substituting the values into the formula, we have:
C = 2π * 60
C ≈ 376.99 cm
Since the hour hand completes one full rotation in 43,200 seconds, the tip of the hand covers a distance equal to the circumference in that time.
Therefore, the tip of the hour hand moves approximately 376.99 cm every second.
To determine the number of centimeters the tip of the hour hand moves each second, we first need to understand how the movement of a clock's hour hand works.
The length of the hour hand represents a radius of a circle, which is equal to the length of the hour hand. The circumference of a circle is calculated using the formula:
Circumference = 2 * π * radius
In this case, the radius of the circle is 60 cm, so we can calculate the circumference as follows:
Circumference = 2 * π * 60 cm
Now, let's determine the number of seconds in one complete revolution of the hour hand. A clock undergoes a full revolution (360 degrees) in 12 hours. Since there are 60 minutes in an hour and 60 seconds in a minute, there are 60 * 60 = 3600 seconds in one hour.
Therefore, the number of seconds in one revolution of the hour hand is 12 * 3600 = 43200 seconds.
To find out how many centimeters the tip of the hour hand moves each second, we divide the circumference by the number of seconds in one complete revolution:
Circumference / Seconds = (2 * π * 60 cm) / 43200 s
Using this formula, we can calculate the exact distance the tip of the hand moves each second.