A biker rides 700 m north and then 300 m east. The total distance traveled is 1000 m (700 + 300). However, displacement — the straight-line distance from start to finish — is 100√58 m ≈ 761.6 m, directed at an angle of approximately 23.2° east of north. This is a standard application of the Pythagoras theorem to vector problems in physics.
Distance traveled = 700 + 300 = 1000 m.
Displacement = √(700² + 300²) = √580,000 = 100√58 ≈ 761.6 m.
Direction of displacement: tan⁻¹(300/700) = tan⁻¹(3/7) ≈ 23.2° East of North.
North and East directions are perpendicular (90°) — Pythagoras theorem applies.
Displacement is always ≤ distance; here displacement < distance because path is L-shaped.
Distance is scalar; displacement is vector (has direction).
Given: • The biker first travels 700 m North • Then travels 300 m East
Part 1 — Total Distance: Distance = sum of all path lengths Distance = 700 + 300 = 1000 m
Part 2 — Displacement (magnitude): The two paths are perpendicular (North ⊥ East). Using Pythagoras theorem: Displacement² = (700)² + (300)² = 490,000 + 90,000 = 580,000
Displacement = √580,000 = √(10,000 × 58) = 100√58 ≈ 100 × 7.616 ≈ 761.6 m
Part 3 — Direction of Displacement: The displacement vector points from Start to End. tan θ = (East component) / (North component) tan θ = 300 / 700 = 3/7 ≈ 0.4286 θ = tan⁻¹(3/7) ≈ 23.2°
Direction: 23.2° East of North (i.e., N 23.2° E)
Final Answer: • Distance = 1000 m • Displacement = 100√58 m ≈ 761.6 m at 23.2° East of North
Visualising the path:
(End point)
|
700m | (North)
|
(Start) ───────── (After going east) 300m (East)
Actually the correct diagram:
Start → 700m North → Turn right → 300m East → End point
The displacement is the straight diagonal from Start to End:
End point is: • 700 m North of start • 300 m East of start
The displacement vector (diagonal) has: • Magnitude = √(700² + 300²) = 100√58 ≈ 761.6 m • Direction = tan⁻¹(300/700) ≈ 23.2° from North towards East
Key concepts: • Distance: total path length (scalar) = 1000 m • Displacement: straight-line vector from initial to final position = 761.6 m at 23.2° E of N • Distance ≥ Displacement always • Displacement = Distance only when motion is in a straight line
Distance vs Displacement:
Distance: • Total path length traveled • Scalar (magnitude only, no direction) • Always positive • Here: 700 + 300 = 1000 m
Displacement: • Shortest straight-line path from initial to final position • Vector (has both magnitude and direction) • Can be less than distance, equal to it (straight-line motion), or zero (return to start) • Here: 100√58 ≈ 761.6 m, at 23.2° East of North
Why displacement < distance here: • The biker changes direction (turns from North to East) • The actual path is L-shaped • The shortest path (displacement) cuts across the corner
Pythagoras theorem application: Whenever two displacement vectors are perpendicular (90°), the resultant displacement is given by: R = √(A² + B²) This is directly from the Pythagorean theorem.
The displacement is 100√58 m ≈ 761.6 m at 23.2° East of North. Using Pythagoras theorem: displacement = √(700² + 300²) = √(490000 + 90000) = √580000 = 100√58 ≈ 761.6 m. The direction is tan⁻¹(300/700) = tan⁻¹(3/7) ≈ 23.2° East of North.
Total distance = 700 + 300 = 1000 m. Distance is the total path length regardless of direction. The displacement (straight-line from start to end) is different: ≈761.6 m at 23.2° East of North.
Because the biker changes direction — the path is L-shaped (first north, then east). The displacement (straight-line from start to finish) cuts across the corner and is shorter than the total L-shaped path. Displacement equals distance only when motion is in a straight line.
The direction angle θ from North = tan⁻¹(East component / North component) = tan⁻¹(300/700) = tan⁻¹(3/7) ≈ 23.2°. So the displacement is directed 23.2° East of North (written as N 23.2° E).
Sign Convention for Spherical Mirrors and Lenses
Learn the New Cartesian Sign Convention for spherical mirrors and lenses. Understand when focal length (f) and image distance (v) are positive or negative.
Simple Harmonic Motion — Equation and Key Formulas
Learn the SHM equation x = A sin(ωt + φ). Understand velocity, acceleration, time period formulas and energy in simple harmonic motion for Class 11 Physics.
What is a Simple Microscope?
Learn what a simple microscope is in Physics. Understand how a single convex lens acts as a magnifying glass to see small objects, and explore its common uses.
What is the SI Unit of Density?
Learn the SI unit of density. Understand the formula (Mass/Volume), its standard unit (kg/m³), and the CGS unit (g/cm³).
What is the SI Unit of Electric Charge?
Learn the SI unit of electric charge. Understand what a Coulomb is, the charge of a single electron, and the formula Q = It.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.