Examkin

Soru

Zorluk: KolayDirection and Distance Test

A field researcher starts from a campsite and walks 10 km10\text{ km} due North. She then turns right and walks 7 km7\text{ km} due East. Next, she turns left and walks 6 km6\text{ km} due North. Finally, she turns right and walks 5 km5\text{ km} due East. What is the shortest straight-line distance (in km) from her final position to the campsite?

Cevap: 20 km

Cevap

The shortest straight-line distance from the final position to the campsite is 20 km.
The researcher ends up 16 km16\text{ km} North and 12 km12\text{ km} East of her starting position. Using the right-triangle distance formula North2+East2\sqrt{\text{North}^2 + \text{East}^2}, we get 162+122=400=20 km\sqrt{16^2 + 12^2} = \sqrt{400} = 20\text{ km}.

Adım Adım Çözüm

1
Sum up the individual directional movements along the North-South axis.
Total North displacement = 10 km+6 km=16 km North10\text{ km} + 6\text{ km} = 16\text{ km North}.
Both vertical moves are towards the North, so their distances add together directly.
2
Sum up the individual directional movements along the East-West axis.
Total East displacement = 7 km+5 km=12 km East7\text{ km} + 5\text{ km} = 12\text{ km East}.
Both horizontal moves are towards the East, so their distances add together directly.
3
Calculate the hypotenuse using the Pythagorean theorem.
Shortest distance = 162+122=256+144=400=20 km\sqrt{16^2 + 12^2} = \sqrt{256 + 144} = \sqrt{400} = 20\text{ km}.
The net North and East displacements form a right-angled triangle where the shortest distance is the hypotenuse.

Anahtar Kavram

Displacement Vector Summation and Pythagorean Distance Calculation
Tahmini Süre:50s
Bu soruyu puanla

Konular

Direction and Distance Test

Bu konudan daha fazla soru