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ACT Exam  >  ACT Questions  >  An object makes a displacement of 4 m due Eas... Start Learning for Free
An object makes a displacement of 4 m due East from a point P and then makes displacement of 3 m due North. Its resultant displacement from P.
  • a)
    7 m
  • b)
    1 m
  • c)
    5 m
  • d)
    1.2 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
An object makes a displacement of 4 m due East from a point P and then...
Let the point 4m from east of P be A. So PA is 4m and the point in the north be B such that AB is 3m. Therefore PBA is a right-angled triangle. The resultant displacement is equal to PB
PA2 + AB2 = PB2
42 + 32 = PB2
16 + 9 = 25 = PB2
PB = 5m
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Most Upvoted Answer
An object makes a displacement of 4 m due East from a point P and then...
Understanding the Problem
The object moves in two perpendicular directions: first 4 m due East and then 3 m due North. To find the resultant displacement, we can visualize this scenario as a right-angled triangle.
Displacement Breakdown
- First Displacement: 4 m East
- Second Displacement: 3 m North
Visualizing the Triangle
- The Eastward displacement forms one side of the triangle (4 m).
- The Northward displacement forms the other side of the triangle (3 m).
- The resultant displacement is the hypotenuse of this right triangle.
Calculating the Resultant Displacement
To find the hypotenuse (resultant displacement), we can apply the Pythagorean theorem:
- Resultant Displacement = √(East Displacement² + North Displacement²)
Substituting the values:
- Resultant Displacement = √(4² + 3²)
- Resultant Displacement = √(16 + 9)
- Resultant Displacement = √25
- Resultant Displacement = 5 m
Conclusion
The resultant displacement from point P is indeed 5 m. Therefore, the correct answer is option 'C'.
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An object makes a displacement of 4 m due East from a point P and then makes displacement of 3 m due North. Its resultant displacement from P.a)7 mb)1 mc)5 md)1.2 mCorrect answer is option 'C'. Can you explain this answer?
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