Question

A cave explorer travels 3.0 m eastward, then 2.5 m northward, and finally 15.0 m westward. use the graphical method to find the magnitude of the net displacement. scale: ________________ magnitude: ___________________ direction: ____________________ can someone help me please i have an exammm tomorrow and i dont know who to solve it ...

Answer 1

Answer:

12.26 m, north-west

Explanation:

From the figure the displacement can be calculated by the Pythagorean law. In this the triangle ABC is the right angle triangle with hypotenous h, base 12 m, and height 2.5 m.

Therefore,

$h^{2}=12^{2}+2.5^{2}\\ h=\sqrt{150.65} \\h=12.26m$

Therefore the net displacement is 12.26 m and the displacement we know it is vector quantity and it is the shortest distance between the two points.

Therefore the displacement is from point B to A. Then the net displacement is the direction in the north-west direction with a magnitude of 12.26 m.

Answer 2

3m east and 15m west evens out to 12m west. That's one side of a triangle. The second side is 2.5m north.
The third side is your displacement,
use Pythagorean's Theorem to determine this.
 a^2+b^2=c^2, that works out to 12^2+2.5^2=c^2.....144+6.25=c^2
150.25=c^2
and
finally
c=12.26,
or 12m