A person travelled 3m East and then 4m north. Find the distance he travelled and also his displacement.
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Answers
Explanation:
using Pythagoras theorem,
Hypotenuse²= Perpendicular² +Base²
= 4²+3²
= 12+9
Hypotenuse= √25
= 5
Hypotenuse= Displacement
therefore displacement= 5m
Distance= (3+4)
= 7m
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Given Information :
• A person travelled 3m East and then 4m north.
To calculate :
• Distance travelled.
Calculation :
Consider the figure in the attachment.
★ Calculating distance travelled :
As we know that,
- Distance is the total path covered by the body.
So,
→ Distance travelled = AB + BC
→ Distance travelled = 3 m + 4 m
→ Distance travelled = 7 m
Therefore, distance covered by the person is 7 m.
★ Calculating displacement :
- Displacement is the shortest path between its final and its initial position.
Its final position is point C and initial position is point A. The shortest distance between point A and point C is AC.
We can also say in ∆ ABC, AC is the hypotenuse. Applying pythagoras property we get,
→ AC² = AB² + BC²
→ AC² = (3m)² + (4m)²
→ AC² = 9m² + 16m²
→ AC² = 25 m²
→ AC = √(25 m²)
→ AC = 5 m
→ Displacement = 5 m
Therefore, displacement is 5 m.
More Information :
About Distance :
- Distance is the length of the total path covered by a body irrespective of the direction in which it travels.
- It is a scalar quantity i.e, it has only magnitude.
- Its SI unit is m (Metre).
- Distance is denoted by "s".
About Displacement :
- Displacement is the shortest path between the final and the initial position of the body.
- It is a vector quantity i.e it has both magnitude and direction.
- Its SI unit is m (Metre).
- Displacement is also denoted by "s".
Points to remember :
• When the body comes again to its starting point or inital position after covering certain distance, then its displacement is 0.
