Sudhir walks 0.40 km in a direction 60.0° west of north, then goes 0.50 km due west. What is his displacement?

The displacement of Sudhir is 0.781 km.

Explanation:

Given;

initial distance, d₁ = 0.4 km = 400 m, N60.0°W

final distance, d₂ = 0.5 km

Make a sketch of Sudhir motion to form a right angled triangle;

(Check image uploaded).

Apply cosine rule to determine d "displacement"

d² = 500² + 400² - (2 x 500 x 400 x cos 120)

d² = 410,000 - (400,000 x -0.5)

d² = 410,000 - (-200,000)

d² = 410,000  + 200,000

d² = 610,000

d = √610000

d = 781.03 m

d = 0.781 km

Therefore, the displacement of Sudhir is 0.781 km.

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