Question

Bhuvi jogs a circular ground of
diameter 14 km..Find the distance and
displacement covered by her in
a. 3 rounds
b. 2 1/2 rounds
c 4 1/4 rounds
d. 1 3/4 rounds

Answer 1

Given:-

Bhuvi jogs a circular ground of  diameter 14 km

To Find:-

the distance and  displacement covered by her in

a. 3 rounds

b. 2 1/2 rounds

c 4 1/4 rounds

d. 1 3/4 rounds

Solution:-

Radius (r) = diameter/2 = 14/2 = 7 km

a. 3 rounds-

Distance covered in 1 round = 2πr = 2x22/7x7 = 44 km

Distance covered in 3 rounds = 3 x 44 = 132 km

Displacement is the shortest distance between the initial and the final position

Displacement covered in 3 rounds = 0 (Since the initial position coincides with the final position)

b. 2 1/2 rounds

Distance covered = 2.5 x distance covered in 1 round = 2.5 x 44 = 110 km

In 2.5 rounds, Bhuvi will reach the other end of the semicircular path

⇒ Displacement =2r = 14 km

Hence the distance and displacement covered at the end of 21/2 rounds is 110 km and 14 km respectively.

c. 4 1/4 rounds-

Distance covered = (4 x distance covered in 1 round + 1/4 x distance covered in one round) = (4x44 + 1/4 x 44) =187 km

Displacement covered = $\sqrt{2}r$ = 7$\sqrt{2}$ km

hence, the distance and displacement covered at the end of 4 1/4 rounds is 187 km and 7$\sqrt{2}$ km respectively.

d. 1 3/4 rounds

Distance covered = (Distance covered in one round + 3/4x distance covered in one round)

= (44+ 33) = 77km

Displacement covered = $\sqrt{2}$r = 7

Hence, the distance and displacement covered at the end of 1 3/4 rounds is 77 km and 7$\sqrt{2}$ km respectively

Answer 2

Given : Bhuvi jogs a circular ground of diameter 14 km..

To Find : the distance and displacement covered by her in

a. 3 rounds

b. 2 1/2 rounds

c 4 1/4 rounds

d. 1 3/4 rounds

Solution:

Diameter = 14 km => Radius  = 14/2 = 7 km

circumference = 2πR = 2 * (22/7) * 7 = 44 km

=> Distance in one round = 44  km

Distance

3 round = 44 * 3 = 132 km

2 1/2 rounds = 44 * 2.5  = 110 km

4  1/4  round = 44 * 17/4  = 187 km

1 3/4 round = 44 * 7/4  = 77 km

Displacement is the least distance between 2 points.

Displacement

3 round  = 0   ( as returns to original position)

2 1/2 round = Diamter = 14 km   as opposite end

4 1/4 round = 7√2  km    as both radius are at right angle

1 3/4 round = 7√2  km    as both radius are at right angle

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