Question

Question 1 (1 point)

A boy on a treasure hunt walks 12 paces West, then 21 paces North, then 25 paces
East. What is the magnitude of boy's resultant displacement in meters?

Answer 1

The magnitude of the boy's displacement is 24.698 paces which is in the direction of approximately 58.24° North of East

Step-by-step explanation:

The given parameters are;

The distance West the boy on a treasure hunt walks = 12 paces

The distance North the boy on a treasure hunt then walks = 21 paces

The distance East the boy on a treasure hunt then walks = 25 paces

Writing the displacement in vector format, gives;

d = -12·i + 21·j + 25·i

Which gives

d = 13·i + 21·j

The magnitude of the boy's resultant displacement is given as follows;

`\left | \mathbf{d} \right | = √(d_x^2 + d_y^2)`

Where;

`d_x = 13, \ d_y = 21`

`\left | \mathbf{d} \right | = √(13^2 + 21^2) = √(610) \approx 24.698 \ paces`

The magnitude of the boy's displacement is 24.698 paces

The direction of the displacement is tan⁻¹(21/13) ≈ 58.24° North of East.