151k views
1 vote
You walk 30 m south and 30 m east. Find the magnitude and direction of the resultant displacement algebraically. (hint: don’t forget to establish your coordinate system).

1 Answer

2 votes

Final answer:

To find the resultant displacement, establish a coordinate system and add the displacements vectorially. The magnitude is approximately 42.4 m and the direction is 135° east of north.

Step-by-step explanation:

To find the magnitude and direction of the resultant displacement algebraically, we need to establish a coordinate system. Let's consider the north direction as positive y-axis and east direction as positive x-axis.

First, we walk 30 m south, which means a displacement of -30 m along the y-axis. Then, we walk 30 m east, which means a displacement of +30 m along the x-axis.

To find the resultant displacement, we can add these two displacements vectorially. The magnitude of the resultant displacement can be found using the Pythagorean theorem: magnitude = sqrt((-30)^2 + 30^2) = sqrt(900 + 900) = sqrt(1800) ≈ 42.4 m.

The direction of the resultant displacement can be found using trigonometry. We can calculate the angle θ using the equation tan(θ) = opposite/adjacent. In this case, θ = tan^(-1)(opposite/adjacent) = tan^(-1)(-30/30) = -45°. However, since we established the north direction as positive y-axis, we need to convert this to a positive angle. So, the direction of the resultant displacement is 180° - 45° = 135° east of north.

User Hoan Dang
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories