Question

While flying due east at 33 m/s an airplane is also being carried due north at 12km by the wind. What is the magnitude of the plane’s resultant velocity?

Answer 1

To find the plane's resultant velocity, convert the northward wind speed to meters and use the Pythagorean theorem with the eastward velocity. Calculate the square root of the sum of the squares of both components to find the magnitude.

Step-by-step explanation:

The student's question pertains to calculating the magnitude of the resultant velocity of an airplane subject to dual movement, which is a classic problem in vector addition in physics. To solve for the resultant velocity, we can use the Pythagorean theorem since the eastward and northward velocities are perpendicular to each other. However, it's important to convert the northward wind velocity from kilometers to meters to match the units of the airplane's eastward velocity.

First, convert 12 km to meters: 12 km * 1000 m/km = 12000 m.
Given the eastward velocity (vx) is 33 m/s and the northward velocity (vy) is 12000 m/s, we can find the magnitude of the resultant velocity (vr) using the Pythagorean theorem: vr = √(vx2 + vy2).

Plugging in the values, the calculation becomes:
vr = √((33 m/s)2 + (12000 m/s)2),
which, upon calculating, gives us the magnitude of the plane's resultant velocity.