# A long hand of a clock measures 28 cm. find the distance & displacement of the long hand from 4.00 pm to 5.30 pm .

2
by debdanMatthai878

2015-05-14T17:42:33+05:30
Let the length of long hand be the radius of the clock
first find the cicumference of the clock by the formula
C = 2 pi r
C = 2 x 22/7 x 28
C = 2 x 22 x 4
C = 44 x 4
C = 176

one div = 14.6
for 4 pm to 5:30
= 14.6 x 1.5
= distance= 7.3 cm
= displacement = 0 cm
2015-05-16T14:20:11+05:30

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See the diagram.

the long hand AB of the clock has two ends.  One end A is fixed at the center of the circle in which the other end B of the hand rotates.

The radius R of the circle in which the tip of the long hand moves = length of the hand.
R = 28 cm.

At 4 pm and at 5:30 pm the long minutes hand of the clock is in positions AB and AB'.  BAB' is a straight line.

The long hand (minutes hand) moves 360 deg. in 1 hour.  So in one and half hours, it rotates  360° * 1.5 = 540°  or  3 π radians.

The angular displacement θ of the clock hand
= angle BAB' = 180 degrees = π radians

The total distance traveled by the tip of the hand B
= 1.50 * perimeter of the circle    (as B makes 1 complete revolution and 1/2 revolution)
= 1.50 * 2 π R
= 3 * 22/7 * 28 cm
= 264 cm

The net displacement traveled by the tip of the hand B
= 1/2 * perimeter of the circle        (as B moves from 0 to 6).
= 1/2 * 2 π R
= 22/ 7 * 28 cm
= 88 cm
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