Question

on a day the wind is blowing towards the south at 7 m/s, a runner jogs west at 7 m/s. what is the velocity (speed and direction) of the air relative to the runner?

Answer 1

Velocity is the rate of change of position of an object. The velocity of the air relative to the runner is 5√2 m/sec and it is in the southwest direction.

What is Velocity?

Velocity is the directional speed of a moving object as an indicator of its rate of change in location as perceived from a certain frame of reference and measured by a specific time standard.

Given that on a day the wind is blowing towards the south at 7 m/s, a runner jogs west at 7 m/s. Therefore, the velocity of the air relative to the runner can be written as,

Relative velocity = √[(Velocity of the jogger)² + (Velocity of the air)²]

                            = √[(5)² + (5)²]

                            = √(25 + 25)

                            = √50

                            = 5√2 m/sec

The direction of the relative velocity is,

The angle of relative Velocity = Tan(θ)

Tan(θ) = Vertical velocity / Horizontal velocity

Tan(θ) = 5/5

Tan(θ) = 1

θ = tan⁻¹(1)

θ = 45°

Since this angle is formed between the two velocities, therefore, the direction of the velocity is southwest.

Hence, the velocity of the air relative to the runner is 5√2 m/sec and it is in the southwest direction.

Learn more about Velocity here:

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