The displacement is 11.2 feet [tex]26.6^{\circ}[/tex] north of west
Explanation:
Displacement is a vector quantity that connects the initial position to the final position of the motion of an object.
Since it is a vector, it has both a magnitude and a direction:
In this problem, the motion of Adam is:
10 feet north
10 feet west
5 feet south
This means that the final position along the north-south direction is
[tex]d_y = +10 +(-5) = +5 ft[/tex] (north, taken as positive direction)
While the final position along the east-west direction is
[tex]d_x = 10 ft[/tex] (west)
Therefore, the magnitude of the displacement is given by Pythagorean's theorem:
[tex]d=\sqrt{d_x^2+d_y^2}=\sqrt{10^2+5^2}=11.2 ft[/tex]
And the direction is given by
[tex]\theta=tan^{-1}(\frac{d_y}{d_x})=tan^{-1}(\frac{5}{10})=26.6^{\circ}[/tex] north of west
Learn more about displacement:
brainly.com/question/3969582
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