Terrence goes for a walk.He walks 2.0 km north,then turns and walks 4.0 km south of east.What is his displacement vector? Take east to be in the +
-direction and north to be in the +
-direction.
A)(2.0 + 4.0 )km
B)(2.8 - 0.8 )km
C)(4.8 + 5.7 )km
D)(5.7 - 2.8 )km

Question

Terrence goes for a walk.He walks 2.0 km north,then turns and walks 4.0 km south of east.What is his displacement vector? Take east to be in the + 
-direction and north to be in the + 
-direction.
A)(2.0 + 4.0 )km 
B)(2.8 - 0.8 )km 
C)(4.8 + 5.7 )km 
D)(5.7 - 2.8 )km

Quizplus · Accepted Answer

The displacement vector is the straight line distance between the starting point and ending point. We can use Pythagoras theorem to find the magnitude of the displacement vector and we can use trigonometry to find its direction.

First, we can find the horizontal and vertical components of the displacement vector using the given distances:
Horizontal component = 4.0 km cos(45°) = 2.8 km
Vertical component = 2.0 km + 4.0 km sin(45°) = 4.8 km

Using Pythagoras theorem, the magnitude of the displacement vector is:
Magnitude = √(2.8 km)² + (4.8 km)² = 5.6 km

Using trigonometry, the direction of the displacement vector is:
Direction = tan⁻¹(4.8 km / 2.8 km) = 59° north of east

Therefore, the displacement vector is (2.8 11ea800b_18e7_c80e_846e_5752c8ea965c_TB6864_11 - 0.8 11ea800b_18e7_c80f_846e_0942631018e6_TB6864_11) km, which corresponds to Choice B.

Terrence Goes for a Walk