Inspirational Physics Problem Solving: Finding Resultant Velocity of an Airplane
How do we calculate the magnitude of the resultant velocity of an airplane experiencing a crosswind?
Given that the airplane heads due north at v₁ = 10m/s and there is a v₂ = 7m/s crosswind blowing from east to west.
Calculating the Magnitude of Resultant Velocity
To calculate the magnitude of the resultant velocity of the airplane, we use the Pythagorean theorem since the velocities are perpendicular to each other.
The magnitude of the resultant velocity (Vr) is calculated using the formula:
Vr = √(v1² + v2²)
Plugging in the given values:
Vr = √(10² + 7²) = √(100 + 49) = √149 ≈ 12.2 m/s
Interpreting the Result
By calculating the magnitude using the Pythagorean theorem, we find that the resultant velocity of the airplane is approximately 12.2 m/s.