Question

An explorer starts hiking from base camp 2 mi north, then he walks for a while in a direction 30 degrees east of north, then he walks 4 mi in a direction 60 degrees south of east, finally, he walks in a direction 12.62 degrees south of west back to base camp. Determine the magnitudes of his second and fourth displacement.

Answer 1

Let initial displacement is

Let second displacement is =>

Let third displacement is =>

Let fourth displacement is

As he reaches his camp again then net displacement is zero.

Considering individual components,

=> ----------------1

=> -----------2

On multiplying equation 1 with 2 => =>

Then substituting S₂ in equation 2;

=> =>

Then from => =>

The second displacement is nearly 2.54 mile and the fourth displacement is nearly 3.35 mile.