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.
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A cyclist travels a distance of 4km from P to Q and then moves a distance of 3 km at right angle
Verified answer
[tex]\huge{\underline{\underline{\red{\bf{Given:}}}}}[/tex]
[tex]\rule{200}4[/tex]
[tex]\huge{\underline{\underline{\red{\bf{To\: Find:}}}}}[/tex]
[tex]\rule{200}4[/tex]
[tex]\huge{\underline{\underline{\red{\bf{Answer:}}}}}[/tex]
(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
Explanation:
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