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avanturin [10]
3 years ago
10

3. An airplane is heading north with an airspeed of 325 m/s with a wind from the east at 55.0 m/s. What is the airplane's veloci

ty relative to the ground? Is the airplane's ground speed faster or slowerthan its air speed? Why?​
Physics
1 answer:
liraira [26]3 years ago
3 0

Let <em>a</em> denote the airplane's velocity in the air, <em>g</em> its velocity on the ground, and <em>w</em> the velocity of the wind. (Note that these are vectors.) Then

<em>a</em> = <em>g</em> + <em>w</em>

and we're given

<em>a</em> = (325 m/s) <em>j</em>

<em>w</em> = (55.0 m/s) <em>i</em>

Then

<em>g</em> = - (55.0 m/s) <em>i</em> + (325 m/s) <em>j</em>

The ground speed is the magnitude of this vector:

||<em>g</em>|| = √[ (-55.0 m/s)² + (325 m/s)² ] ≈ 330. m/s

which is faster than the air speed, which is ||<em>a</em>|| = 325 m/s.

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