Question

A person moves 30 m north, then 20 m east and then 3root2 m south-west. His displacement from the origin
position is
(1) 14 m south-west
(2) 28 m south
(3) 10 m west
(4) 15 m east​

Answer 1

Explanation:

Correct Question :-

A person moves 30 m North, then 20 m east and then 30√2 m south-west. His displacement from the origin position is

1) 14 m south-west

2) 28 m south

3) 10 m west

4) 15 m east

Solution :-

Given -

Person moves :-

• 30 m North
• 20 m east
• 30 √2 m south-west

To Find -

• Displacement from the origin position is what ?

Now,

Person moves :

• 30 m North = 30 j cap
• 20 m east = 20 î (i cap)

30 √2 m south-west,

Here, we take components :-

Along x-axis :-

→ 30√2 cos45°

→ 30√2 × 1/√2

• → 30 î (i cap) [West]

And

Along y-axis :-

→ 30√2 sin45°

→ 30√2 × 1/√2

• → 30 j cap [South]

Now,

Net movement :-

→ 30 j cap + 20 î (i cap) - 30 î (i cap) - 30 j cap

→ - 10 î (i cap)

So,

Displacement is 10 m towards West from origin.

Hence,

Option (3) is correct.