A clock has a minute hand that is 14 feet long and an hour hand that is 9 feet long. What is the average speed (in mph) of the tip of the minute hand
no idea how to solve this... please help :)
That is one monster clock!!
one rotation of the minute hand is
2πr = 2π(14) = 28π ft
so it does 28π ft/ 1 hr
= (28π/5280) mph
= appr .01666 mph
Why would you measure in mph ?
inches/min might be a more useful unit.
wow your a genius! yeah I have no idea either... one more question :) how would you solve backwards to find length of the minute hand if the average speed was 1 mph?
just keep replacing the units
1 mile / 1 hour
= 5280 ft/ 1 hr
= 63360 inches / 1 hr
= 63360 inches / 60 minutes
= 1056 inches/min
etc
To find the average speed of the tip of the minute hand, we need to determine the distance traveled by the tip of the minute hand in a certain amount of time.
First, we need to calculate the circumference of the circle created by the tip of the minute hand. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the radius is equal to the length of the minute hand, which is 14 feet.
C = 2 * π * 14
C ≈ 87.9646 feet
Next, we need to convert the distance traveled by the minute hand to miles. There are 5,280 feet in a mile.
Distance in miles = Distance in feet / 5,280
Distance in miles ≈ 87.9646 / 5280
Distance in miles ≈ 0.01667 miles
Now, we need to determine the time it takes for the minute hand to travel this distance. Since the question doesn't specify a time, we cannot calculate an average speed. We need the time taken to complete the revolution.
Finally, we can calculate the average speed in mph. Since we don't have a specific time frame, we cannot provide an accurate average speed. Average speed is generally calculated by dividing the total distance traveled by the time taken.
Therefore, without knowing the specific time frame, we cannot determine the average speed (in mph) of the tip of the minute hand.