Another boat in a current The water in a river moves south...

Another boat in a current The water in a river moves south at $5 \mathrm{km} / \mathrm{hr.}$ If a motorboat is traveling due east at a speed of $40 \mathrm{km} / \mathrm{hr}$ relative to the water, determine the speed of the boat relative to the shore.

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Key Concepts

Relative Velocity

Relative velocity is a concept that describes how the speed and direction of an object are measured relative to different frames of reference. In problems involving a moving medium, such as water or air, the velocity of an object must be considered relative to both the medium and an external observer, like someone on shore.

Vector Addition

Vector addition is the process used to combine two or more velocity vectors into a single resultant vector. In problems involving motion in multiple directions, each component of motion is represented as a vector, and the overall motion is determined by summing these vectors according to their magnitude and direction.

Pythagorean Theorem

The Pythagorean Theorem is used to determine the magnitude of the resultant vector when the component vectors are perpendicular to each other. After applying vector addition for perpendicular components, the resultant speed is calculated by taking the square root of the sum of the squares of the individual components.

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