Question

A car travels 8km along east then 15km along north and then 15 root 2 km towards (south - west). The displacement of car from starting point is a) 7km b) 24km c) 10km d) 25km



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Answer 1

Hope this helps you

Answer 2

Given:

• The distance along east = 8 Km
• The distance along north = 15 Km
• The distance along south-west = 15√2 Km

To Find:

• The displacement of car from starting point.

Solution:

We are going to convert the displacement given into cartesian form(vector form) since it specifies a particular direction.

1. The first displacement is towards the east which is towards the x-axis.

∴ $D_1$ = 8 km = 8 i → (1)

2. The second displacement is towards the north which is towards the y-axis.

∴ $D_2$ = 15 Km = 15 j → (2)

3. The third displacement is towards the southwest which is towards the negative x-axis and y-axis.

∴$D_3$ = 15√2 Km = -15 i - 15 j → (3)

Now applying the superposition theorem on (1), (2), and (3) we get the total displacement.

⇒ D =  $D_1+D_2+D_3$

⇒ D = 8i + 15j -15i - 15j {cancelling the like terms}

⇒ D = 8i-15j {subtracting the terms}

⇒ D = -7i {applying modulus OBS}

⇒ |D| = 7 Km

∴ The displacement of car from starting point = 7 Km. (option a)