Question

20 calvin is flying on airplane. his velocity with respect to the air around him is 78.0 m/s south. the air is also moving with a velocity of 12.4 m/s east. to an observer on the ground, what is the magnitude of calvins velocity? 90.4 m/s 79.0 m/s 87.6 m/s 62.7 m/s

Explanation:

Step1: Analyze the velocity vectors

Calvin's velocity with respect to air \(v_{c/a}=78.0\ m/s\) (south) and air's velocity with respect to ground \(v_{a/g}=12.4\ m/s\) (east). These two velocities are perpendicular.

Step2: Use Pythagorean theorem

The magnitude of Calvin's velocity with respect to ground \(v_{c/g}\) is given by \(v_{c/g}=\sqrt{v_{c/a}^{2}+v_{a/g}^{2}}\).
Substitute \(v_{c/a} = 78.0\ m/s\) and \(v_{a/g}=12.4\ m/s\) into the formula:

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Answer:

79.0 m/s