Question

Question 1 (1 point)

Answer 1

Answer:

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

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;

$\left | \mathbf{d} \right | = \sqrt{d_x^2 + d_y^2}$

Where;

$d_x = 13, \ d_y = 21$

$\left | \mathbf{d} \right | = \sqrt{13^2 + 21^2} = \sqrt{610} \approx 24.698 \ paces$

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.