Question

Jimmy walks to school by traveling 2.0 miles east and 3.0 miles north from his starting point. What are the magnitude and direction of Jimmy's displacement with respect to his original position?

Answer 1

Answer:

3.6 miles at 56.3 degrees north of east.

Explanation:

If you draw a diagram to calculate Jimmy's displacement, you end up with a triangle.

To solve for the magnitude of Jimmy's displacement with respect to his original position, we need to use the Pythagorean Theorem formula.

Pythagorean Theorem Formula = a^2 + b^2 = c^2

Step by Step to solve for the magnitude of Jimmy's displacement:

1) a^2 + b^2 = c^2

2) 2.0^2 + 3^2 = c^2

3) 4 + 9 = c^2

4) 13 = c^2

5) To find what "c" equals to we need to find the square root of 13.

6) √13 = 3.6 | c = 3.6 miles

To solve for the direction of Jimmy's displacement with respect to his original position, we need to use the following formula:

tan^-1 ∅ (3/2)

tan^-1 ∅ (1.5)

∅ = 56.309° north of east

Therefore, your answer is 3.6 miles at 56.3 degrees north of east.