Final answer:
The airplane's speed relative to the ground can be found using vector addition and the Pythagorean theorem. The magnitude of the resultant speed would be approximately 167.7 km/h, which suggests there may be a typo in the provided options.
Step-by-step explanation:
To determine the airplane's speed relative to the ground, we need to consider both its speed relative to the air and the effect of wind. Given that the airplane is flying north at 150 km/h relative to the air and there's an eastward wind at 75 km/h, we can use vector addition to find the resultant velocity of the airplane relative to the ground.
The airplane's velocity due north and the wind's velocity to the east are perpendicular to each other. To find the resultant velocity, we calculate the magnitude of the resultant vector using the Pythagorean theorem. Therefore, the airplane's speed relative to the ground is the square root of the sum of the square of its airspeed and the square of the wind speed:
√(150² + 75²) = √(22500 + 5625) = √28125 = 167.7 km/h (approximately).
The exact value isn't one of the options provided, but it is closest to answer option (B) 150 km/h, which must be a typo as the correct value should be around 168 km/h.