A cave explorer travels 15 m west, then 25 m north, and finally 3 m east. What is his resultant displacement ?

The resultant displacement of the cave explorer is 12 m west and 25 m north which is approximately 27.73 m in the 64.36° south of east direction from the cave explorer's initial location

Explanation:

The motion of the cave explorer are;

15 m west, 25 m north, and 3m east

The displacement, d, of the cave explorer can be displayed in vector form as follows (Taking east as positive and west as the negative direction of the ordinates);

= 3·i - 15·i + 25·j

∴ = -12·i + 25·j

The resultant displacement of the cave explorer is 12 m west and 25 m north

The magnitude and direction of the resultant displacement of the cave explorer are;

√((-12)² + 25²) ≈ 27.73 m

The direction is tan⁻¹(25/-12)  ≈ -64.36°  North of east = 64.36°  south of east

The magnitude and direction of the resultant displacement of the cave explorer are 27.73 m in a direction 64.36°  south of east.