MHB How far does the tip of the hour hand move in 3 hours?

  • Thread starter Thread starter dtippitt
  • Start date Start date
  • Tags Tags
    Clock hand
Click For Summary
To determine how far the tip of the hour hand moves in 3 hours, the arc length formula is applied. The hour hand, 2 cm long, moves through a quarter of a circle in that time, equivalent to 90 degrees or π/2 radians. The circumference of a circle is calculated as 2πr, leading to a quarter circumference of (1/4) * 2π * 2 cm. This results in a movement of π cm, which is approximately 3.14 cm. Thus, the tip of the hour hand moves about 3.14 cm in 3 hours.
dtippitt
Messages
5
Reaction score
0
How far to the nearest hundreth cm, does the tip of the hour hand on a clock move in exactly 3 hours if the hour had is 2.00 cm long?

I think you are supposed to use arc length formula.

This is what I got so far:

s=r(radian symbol) = 3=1(radian symbol)
 
Mathematics news on Phys.org
Re: Possible trignomery and distance formula

dtippitt said:
How far to the nearest hundreth cm, does the tip of the hour hand on a clock move in exactly 3 hours if the hour had is 2.00 cm long?

I think you are supposed to use arc length formula.

This is what I got so far:

s=r(radian symbol) = 3=1(radian symbol)

the hour hand of an analog clock moves 1/12 of a revolution in one hour.

one revolution is 2pi radians

$s = r \cdot \theta$

take it from here?
 
dtippitt said:
How far to the nearest hundreth cm, does the tip of the hour hand on a clock move in exactly 3 hours if the hour had is 2.00 cm long?

In 3 hours, the hour hand turns through a right angle, i.e. a quarter of a circle. What is a quarter of the circumference of a circle of radius 2 cm?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

Similar threads

  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
1K
Replies
1
Views
5K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
38
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K