A migrating whale follows the coast of Mexico and...

A migrating whale follows the coast of Mexico and California. It first travels $360 \mathrm{~km}$ northwest, then turns due north and travels another $410 \mathrm{~km}$. Determine graphically the magnitude and direction of its displacement.

Key Concepts

Resolving Vectors into Components

Resolving a vector into its components involves breaking the vector down into perpendicular directions, usually along horizontal (x-axis) and vertical (y-axis) directions. This technique simplifies the process of vector addition, as it allows each component to be added separately before recombining them to find the resultant vector.

Trigonometric Methods

Trigonometric methods, including the use of sine, cosine, and the inverse tangent functions, are used to relate the components of a vector to its overall magnitude and direction. This approach is essential for calculating the angle and length of the resultant vector when the individual vector components are known.

Graphical Representation of Vectors

Graphical representation involves drawing vectors on a coordinate system using their magnitudes and directions, often to scale. This visual method allows one to apply geometric techniques, such as the tip-to-tail method, to determine the resultant displacement vector by accurately measuring the distance and angle between points.

Vector Addition

Vector addition is the process of combining two or more vectors to calculate a single resultant vector. This process involves adding equivalent components of the vectors, either graphically or numerically, to determine the overall effect on magnitude and direction.

Displacement

Displacement is a vector quantity that represents the change in position of an object. It has both magnitude and direction, and is typically determined by measuring the straight-line distance from the starting point to the ending point, regardless of the path taken.

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