Question

On a stopwatch, the tip of the second hand moves 2 cm in 15 seconds. How long is the second hand (to the nearest tenth)? A. 1.3 cm. B. 6.3 cm. C. 12.6 cm. D. 30.0 cm

Answer 1

Clever question. Pretty simple, but we never think of the details
quite in this order.

-- The 'seconds' hand on the watch goes all the way around in 1 minute.
The tip of the hand moves in a circle.

-- 15 seconds is 1/4 of a complete 1-minute revolution.
So the 2 cm is 1/4 of the way around the circle that the tip makes.

-- The full circumference of the circle is 8cm.

-- The length of the second hand is the radius of the circle.

2 pi radius = circumference

2 pi radius = 8 cm
Divide each side
by 2 pi : radius = 8cm / 2 pi = 1.27 cm
(choice - A)

Answer 2

we are asked to determine the length of the second hand when it has moved 2 cm in 15 seconds. The movement in 15 seconds generates an angle of 90 degrees or pi / 2. we apply the equation of arc length which is 2 cm; s = 2= r theta = r* pi /2 where r is the second hand length. The answer is 1.27 cm closest to A