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????
algebra - PsyDAG, Sunday, November 13, 2011 at 1:38am
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.
Thanks for your help, but I still didn't get the answer. Speed = distance/time. 5 pi is my distance, so i have to find the time. (which the answer says is 264.) I tried 15s x 1min/60s x 1hr/60min = .004166666 hr
the speed answer is 5pi/264 =approx .0575
The answer of 5π inches/sec is the speed of the ≤b≥second≤/b≥ hand not the minute hand like you asked for.
Is there a misprint?
The minute hand moves 6° or π/30 radians in 1 minute
so in 15 seconds, it moves 1.5° or π/120 radians
arc length = rØ = 10(π/120) = π/12 inches in 15 seconds
So in 15 seconds it would move π/12 inches
speed in inches/sec = π/180 inches/sec
(number of inches in a mile = 12(3)(1760) = 63360
number of seconds in 1 hours = 3600 )
speed in miles/hr = (π/180)(3600/63360) = π/3168
The speed of the minute hand is π/3168 mph
If you want the speed of the second hand multiply that by 60 to get the answer of 5π/264
To find the speed in miles per hour, you need to convert the distance and time from inches and seconds to miles and hours.
First, let's convert the distance from inches to miles. The given distance is 5π inches. To convert this to miles, we can use the conversion factor: 1 mile = 63360 inches.
Therefore, the distance in miles is:
5π inches * (1 mile/63360 inches) = 5π/63360 miles
Next, let's convert the time from seconds to hours. The given time is 15 seconds. To convert this to hours, we can use the conversion factor: 1 hour = 3600 seconds.
Therefore, the time in hours is:
15 seconds * (1 minute/60 seconds) * (1 hour/60 minutes) = 15/3600 hours
Finally, we can calculate the speed by dividing the distance by the time:
Speed = (5π/63360 miles) / (15/3600 hours)
Simplifying this expression gives us:
Speed = (5π * 3600) / (15 * 63360) miles per hour
Calculating this value gives us:
Speed ≈ 0.0575 miles per hour
To calculate the speed in miles per hour, you need to convert the distance traveled by the tip of the minute hand from inches to miles and the time from seconds to hours.
First, you correctly found that the distance traveled by the tip of the minute hand is 5π inches.
To convert inches to miles, you need to divide the distance by the number of inches in a mile. There are 12 inches in a foot and 5280 feet in a mile:
5π inches ÷ (12 inches/foot) ÷ (5280 feet/mile) = 5π/63360 miles
Next, you need to convert the time from seconds to hours. There are 60 seconds in a minute and 60 minutes in an hour:
15 seconds ÷ (60 seconds/minute) ÷ (60 minutes/hour) = 15/3600 hours
Finally, you can calculate the speed by dividing the distance by the time:
Speed = (5π/63360 miles) ÷ (15/3600 hours)
To divide by a fraction, you multiply by the reciprocal:
Speed = (5π/63360 miles) × (3600/15 hours)
Simplifying, you get:
Speed ≈ 0.0575 miles per hour