Questions 1-3 refer to the following scenario: IMAGE IS NOT...

Questions 1-3 refer to the following scenario: IMAGE IS NOT AVAILABLE TO COPY An explorer travels 30 $\mathrm{m}$ east, then 20$\sqrt{2} \mathrm{m}$ in a direction $45^{\circ}$ south of east, and then 140 $\mathrm{m}$ north. What is the displacement of the explorer? (A) 130 $\mathrm{m}$ (B) 169 $\mathrm{m}$ (C) 170 $\mathrm{m}$ (D) 215 $\mathrm{m}$

Questions 1-3 refer to the following scenario:
IMAGE IS NOT AVAILABLE TO COPY
An explorer travels 30 $\mathrm{m}$ east, then 20$\sqrt{2} \mathrm{m}$ in a direction $45^{\circ}$ south of east, and then 140 $\mathrm{m}$ north.
What is the displacement of the explorer?
(A) 130 $\mathrm{m}$
(B) 169 $\mathrm{m}$
(C) 170 $\mathrm{m}$
(D) 215 $\mathrm{m}$

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Key Concepts

Displacement

Displacement is a vector quantity that represents the straight-line change in position from an object's initial location to its final location, taking into account both magnitude and direction. It differs from distance, which is a scalar representing the total path traveled regardless of direction.

Vector Addition

Vector addition is the process of combining multiple vectors to determine a resultant vector. In problems involving several movements with different directions, each vector is added by combining its respective components to find the overall displacement.

Component Method

The component method involves breaking each vector into its horizontal and vertical parts. By resolving vectors into their x and y components, one can simplify the addition process, allowing calculations to be performed separately before recombining the components to find the resultant vector.

Trigonometric Decomposition

Trigonometric decomposition uses sine and cosine functions to resolve a vector with a given magnitude and angle into its horizontal and vertical components. This technique is crucial for accurately handling vectors that are not aligned with the standard axes.

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