The pilot of an airplane notes that the compass indicates a...

The pilot of an airplane notes that the compass indicates a heading due west. The airplane's speed relative to the air is $150 \mathrm{~km} / \mathrm{h}$. If there is a wind of $90.0 \mathrm{~km} / \mathrm{h}$ toward the north, find the velocity of the airplane relative to the ground.

Key Concepts

Relative Velocity

Relative velocity refers to the velocity of an object as measured in a particular reference frame, taking into account the motion of the medium through which it is moving. In the context of an airplane, the plane’s velocity relative to the ground is obtained by combining its velocity relative to the air with the velocity of the wind.

Vector Addition

Vector addition is the process of combining two or more vectors to form a resultant vector. When dealing with motions in different directions, such as an airplane’s heading and wind direction, each velocity is represented as a vector, and these vectors are added component-wise to find the overall or ground velocity.

Component Decomposition

Component decomposition involves breaking down vectors into their perpendicular components, commonly along the north-south and east-west axes. This allows for easier arithmetic when adding vectors, by summing corresponding components separately, which is essential in calculating the resultant velocity of the airplane relative to the ground.

Reference Frames

A reference frame is a coordinate system or perspective from which measurements such as position and velocity are made. In problems involving wind and airplane motion, the airplane's speed with respect to the air (airframe's reference frame) is combined with the wind's speed relative to the ground (ground reference frame) to obtain the airplane’s ground speed.

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