Question

A model airplane is flying North with a velocity of 15 m/s. A strong wind is blowing East at 12 m/s. What is the airplane’s resultant speed (magnitude of velocity vector)?

Answer 1

The resultant speed of the model airplane flying north at 15 m/s with an eastward wind at 12 m/s is calculated using vector addition and the Pythagorean theorem. The magnitude of the resultant velocity is found to be 19.21 m/s.

Step-by-step explanation:

The student's question relates to finding the resultant velocity of a model airplane that is subjected to cross winds while in flight. To calculate this, we can use vector addition, where the velocity of the airplane and wind velocity are treated as vectors.

The airplane is moving north at 15 m/s, and the wind is blowing east at 12 m/s. This forms a right-angled triangle where the northward movement is one side, the eastward wind is the perpendicular side, and the hypotenuse is the resultant speed.

Applying the Pythagorean theorem to this scenario, we can calculate the magnitude of the resultant speed (VR) using the formula:

VR = √(VN2 + VE2)

VR = √((15 m/s)2 + (12 m/s)2)

VR = √(225 + 144)

VR = √(369)

VR = 19.21 m/s (rounded to two decimal places)

The magnitude of the resultant velocity of the airplane is 19.21 m/s.