Question

A cyclist travels a distance of 4km from P to Q and then moves a distance of 3 km at right angle to PQ. Find the displacement and distance traveled by the cyclist.

Answer 1

$\huge{\underline{\underline{\red{\bf{Given:}}}}}$

• A cyclist travels 4km from point P to Q.
• He turns right and then moves 3km.

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$\huge{\underline{\underline{\red{\bf{To\: Find:}}}}}$

• The displacement of the cyclist.
• The distance covered by the cyclist.

$\rule{200}4$

$\huge{\underline{\underline{\red{\bf{Answer:}}}}}$

(For figure refer to attachment)

Given that a cyclist moves 4km from point P to Q, thereafter it turns right and moves 3km.

So, total distance covered = (3+4) km= 7km .

Now, displacement is the shortest distance between the initial and the final point.

Let us say that he reached point R .

So from figure it is clear that the displacement will be equal to the hypotenuse of the right ∆ PQR which is PR .

Now ,

⇒ PR²= QR² + PQ². (By Pythagoras Theorem)

⇒ PR² = (3km)²+(4km)².

⇒PR² = 9km²+16km².

⇒PR² = 25km²

⇒PR =√25km².

⇒PR = 5km.

Hence displacement is 5km

Answer 2

Explanation:

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