An airplane is flying due west at a velocity of 100 m/s. The wind is blowing out of the south at 5 m/s. What is the magnitude of airplane's resultant velocity?

To find the magnitude of the airplane's resultant velocity, we need to use vector addition.

The airplane's velocity, flying due west at 100 m/s, is a vector pointing in the negative x-direction. The wind's velocity, blowing out of the south at 5 m/s, is a vector pointing in the negative y-direction.

To add the two vectors together, we can use the Pythagorean theorem. The magnitude of the resultant velocity can be calculated using the formula:

resultant velocity = √(x^2 + y^2)

Where x is the horizontal component (westward) and y is the vertical component (southward) of the resultant velocity.

In this case, the horizontal component of the resultant velocity is -100 m/s (since it's moving westward) and the vertical component is -5 m/s (since it's blowing out of the south).

Plugging these values into the formula, we get:

resultant velocity = √((-100)^2 + (-5)^2)
= √(10000 + 25)
= √10025
≈ 100.12 m/s

Therefore, the magnitude of the airplane's resultant velocity is approximately 100.12 m/s.

To find the magnitude of the airplane's resultant velocity, we need to consider the vector addition of the airplane's velocity and the wind's velocity.

Since the airplane is flying due west at a velocity of 100 m/s, we can represent its velocity as a vector pointing in the negative x-direction: -100 m/s.

Similarly, since the wind is blowing out of the south at a velocity of 5 m/s, we can represent its velocity as a vector pointing in the negative y-direction: -5 m/s.

To find the resultant velocity, we can use the Pythagorean theorem:

Resultant velocity^2 = (airplane's velocity)^2 + (wind's velocity)^2

= (-100 m/s)^2 + (-5 m/s)^2

= 10000 m^2/s^2 + 25 m^2/s^2

= 10025 m^2/s^2

Taking the square root of both sides gives:

Resultant velocity = √(10025 m^2/s^2)

≈ 100.12 m/s

Therefore, the magnitude of the airplane's resultant velocity is approximately 100.12 m/s.

s^2 = 100^2 + 5^2

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