Question

6. Find distance and displacement of a body in each of the following situations
a) A body travels 25% of the circumference of a circular path having radius “r” cm
b) A body is thrown vertically upward from top of a building which is 30 m tall. The body
goes 5 m high above the top of the building and then falls towards the ground and finally hits
the ground.​

Answer 1

Given:

a) A body travels 25% of the circumference of a circular path having radius “r” cm

b) A body is thrown vertically upward from top of a building which is 30 m tall. The body goes 5 m high above the top of the building and then falls towards the ground and finally hits the ground.​

To find:

Find distance and displacement of a body in each of the above mentioned situations.

Solution:

a)

Circumference of the circle = 2πr

25% of the circumference of a circular path

= 25% × 2πr

= 25/100 × 2πr

= 1/4 × 2πr

= πr/2

∴ The distance covered is πr/2 cm.

As displacement is the shortest distance covered, so we have,

= √ (r² + r²)    (using Pythagoras theorem)

= √(2r²)

= √2r

∴ The displacement is √2r cm.

b)

A body is thrown vertically upward from top of a building which is 30 m tall.

The body goes 5 m high above the top of the building.

⇒ distance = 30 + 5 = 35 m.

∴ The distance is 35 m

and then falls towards the ground and finally hits the ground.​

As the object hits the ground, the displacement is 0.

∴ The displacement is 0 m.