A bicyclist rides along the hard-packed sand beach with a...

A bicyclist rides along the hard-packed sand beach with a speed $v_{B}=16 \mathrm{mi} / \mathrm{hr}$ as indicated. The wind speed is $v_{w}=20 \mathrm{mi} / \mathrm{hr} .(a)$ Determine the velocity of the wind relative to the bicyclist. (b) At what speed $v_{B}$ would the bicyclist feel the wind coming directly from her left (perpendicular to her path)? What would be this relative speed?

A bicyclist rides along the hard-packed sand beach with a speed $v_{B}=16 \mathrm{mi} / \mathrm{hr}$ as indicated. The wind speed is $v_{w}=20 \mathrm{mi} / \mathrm{hr} .(a)$ Determine the velocity of the wind relative to the bicyclist.
(b) At what speed $v_{B}$ would the bicyclist feel the wind coming directly from her left (perpendicular to her path)? What would be this relative speed?

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Key Concepts

Relative Velocity

Relative velocity refers to the velocity of an object as observed from a particular reference frame, calculated by subtracting the velocity of the observer (or platform) from the velocity of the moving object. This concept highlights how motion appears differently depending on the frame of reference used, which is crucial when analyzing situations where both the observer and the object are in motion.

Vector Addition and Subtraction

Because velocity is a vector quantity, its addition or subtraction must consider both magnitude and direction. In problems involving relative motion, one subtracts the velocity vector of the observer from the velocity vector of another object to determine how that object appears to move from the observer’s standpoint.

Component Decomposition

When dealing with vectors that are not aligned, it is often necessary to decompose them into their perpendicular components (usually horizontal and vertical). This process simplifies analysis and calculation, as each component can be handled separately, allowing conditions (such as making one component zero) to be applied when analyzing specific directions of motion.

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