A football player runs 11m [N20E]. He then changes direction and then runs 9m [E]. What is his total displacement?

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The football player runs 11m in a direction N20E. He then changes direction and then runs 9m towards the east.

To find the displacement of the player, divide the initial 11m run in the direction N20E into components in the East and the North. These are 11*cos 20 towards the North and 11*sin 20 towards the East.
He later runs 9 m towards the East. The total displacement towards the East is 11*sin 20 + 9 = 12.7622 m and the total displacement towards the North is 10.336 m

The magnitude of the displacement of the player is `sqrt(12.7622^2 + 10.336^2)` = 16.42 m

The direction of displacement is `tan^1(12.7622/10.336)` = 50.99 degrees East of North

The displacement of the player is 16.42 m [N51E]

Approved by eNotes Editorial Team
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