A Strong wind blows to the west at a speed of 38.7 mph relative to the ground causing a commercial plane to change course. What should be the plane's velocity in order to maintain a southward direction at a constant speed of 452 mph relative to the ground?

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MrRoyal MrRoyal · Answer 1 · 2021-11-19T13:56:15+01:00

The speed of the plane is the rate of change of distance over time

The speed of the plane should be 453.65 mph southwest

The speed of the wind is given as:

[tex]\mathbf{S_w = 38.7mph}[/tex]

The expected speed of the plane is:

[tex]\mathbf{S_s = 452mph}[/tex]

So, the actual speed is calculated using the following Pythagoras theorem

[tex]\mathbf{S_{sw}^2 = S_w^2 + S_s^2}[/tex]

This gives

[tex]\mathbf{S_{sw}^2 = 38.7^2 + 452^2}[/tex]

[tex]\mathbf{S_{sw}^2 = 205801.69}[/tex]

Take square roots of both sides

[tex]\mathbf{S_{sw} = 453.65}[/tex]

Hence, the speed of the plane should be 453.65 mph southwest