Minute hand of a clock is 10 inches long.
how far does the tip of the minute hand move in 15 seconds?
I got that=5 pi
BUT What speed is it moving in miles/hr????
Assuming it does move 5 pi, convert 5 * 3.1416 = 15.7 inches to portions of a mile. Convert 15 seconds into a portion of an hour, then increase both so divisor is a complete hour.
To determine the speed at which the tip of the minute hand moves, we need to calculate the distance covered in 15 seconds and then convert it to miles per hour.
First, let's calculate the circumference of the circular path traced by the tip of the minute hand. The circumference of a circle is given by the formula:
C = 2πr
where C is the circumference and r is the radius. In this case, the radius is 10 inches, so the circumference is:
C = 2π(10) = 20π inches
Next, we need to find out how much of the circumference is covered in 15 seconds. To do this, we need to determine the fraction of time that 15 seconds represents compared to a full rotation of the minute hand.
In one minute (60 seconds), the minute hand completes a full rotation. Therefore, in 15 seconds, the fraction covered is:
Fraction covered = 15/60 = 1/4
Finally, we can calculate the distance covered in 15 seconds:
Distance covered = Fraction covered * Circumference
= (1/4) * 20π
= 5π inches
Now, to convert this distance from inches to miles, we can use the conversion factor: 1 mile = 63,360 inches.
Distance covered in miles = (5π inches) / (63,360 inches/mile)
= 5π / 63,360 miles
Simplifying this, we get:
Distance covered in miles ≈ 0.000249561 miles
To find the speed in miles per hour, we divide this distance by 15 seconds (converted to hours):
Speed = (0.000249561 miles) / (15 seconds / 3600 seconds/hour)
= (0.000249561 miles) / (0.0041667 hours)
≈ 0.0599 miles per hour
Thus, the speed at which the tip of the minute hand moves is approximately 0.0599 miles per hour.
To find the speed of the tip of the minute hand in miles per hour, we need to convert the distance it moves in 15 seconds to miles and the time taken to hours.
First, let's calculate the distance the tip of the minute hand moves in 15 seconds.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the minute hand acts like the radius of a circle with a length of 10 inches.
So, the distance the tip of the minute hand moves in 15 seconds is equal to the arc length of a circle with a radius of 10 inches over a central angle of 15 seconds.
The formula to calculate the arc length is given by the equation L = θr, where L is the arc length, θ is the central angle in radians, and r is the radius.
To convert seconds to radians, we need to use the fact that there are 60 seconds in a minute and 2π radians in a circle.
So, the central angle in radians is (15/60) * 2π = (1/4) * 2π = π/2.
Now, we can calculate the arc length: L = (π/2) * 10 = 5π inches.
To convert the distance from inches to miles, we need to divide it by the number of inches in a mile. There are 12 inches in a foot and 5280 feet in a mile, so there are 12 * 5280 = 63,360 inches in a mile.
Now, let's perform the conversion: 5π inches / 63,360 inches/mile = (5π) / 63,360 miles.
To find the speed, we need to divide the distance by the time. In this case, the time is 15 seconds, but we need to convert it to hours.
There are 60 seconds in a minute and 60 minutes in an hour, so there are 60 * 60 = 3600 seconds in an hour.
Let's perform the conversion: 15 seconds / 3600 seconds/hour = 15 / 3600 hours.
To calculate the speed, divide the distance by the time:
[(5π) / 63,360 miles] / (15 / 3600 hours) = [(5π) / 63,360] * (3600 / 15) = π * (2400 / 63,360) = π * (2 / 53) ≈ 0.1185π miles per hour.
So, the speed of the tip of the minute hand is approximately 0.1185π miles per hour.