A sail boat sails $$2$$ km due East, $$5$$ km $$370$$ South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is $$6$$ km due East, determine the third displacement.

Question

A sail boat sails $$2$$ km due East, $$5$$ km $$370$$ South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is $$6$$ km due East, determine the third displacement.

Infinity Learn · Accepted Answer

(a) Given resultant displacement is $$6$$ km due eastWhich may be expressed as $$6i^Given$$ displacement $$are(i)$$ $$2$$ km due east or $$2i^(ii)$$ $$5$$ km $$370$$ south of east its componentsalong $$x-axis$$ $$=$$ $$5$$ $$cos$$ $$370$$ $$=$$ $$5$$×$$45$$ $$=$$ $$4i^along$$ $$y-axis$$ $$=$$ $$5$$ $$sin370$$ $$=$$ $$5$$×$$35$$ $$=$$ $$-3j^(iii)$$ unknown displacement let it be $$ai^+bj^$$∴  $$2i^+4i^$$−$$3j^+$$ $$ai^+bj^$$  $$=$$  $$6i^$$∴  $$6i^+$$ $$ai^$$−$$3j^+bj^$$  $$=$$  $$6i^comparing$$ the two sidesa $$=$$ $$0$$ and b $$=$$ $$3$$∴ unknown displacement $$=$$ $$3j^$$

A sail boat sails 2 km due East, 5 km $37^{0}$ South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.

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A sail boat sails 2 km due East, 5 km 370 South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.

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Ready to Test Your Skills?

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A sail boat sails 2 km due East, 5 km $37^{0}$ South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.