a plane is flying at 190 m/s in the y-direction. The wind is blowing at 25.0 m/s in the x- direction. What is the magnitude of the velocity of the plane?

Question

v=[?] m/s

Answer 1

To determine the magnitude of the velocity of the plane, we need to consider both components of the plane's velocity: its velocity in the \( y \)-direction and the wind's velocity in the \( x \)-direction. Since these two components are perpendicular to each other, we can use the Pythagorean theorem to find the resultant velocity.

Given:
- Plane's velocity in the \( y \)-direction (\( v_y \)) = 190 m/s
- Wind's velocity in the \( x \)-direction (\( v_x \)) = 25.0 m/s

The formula to find the magnitude of the resultant velocity (\( v \)) is:
\[ v = \sqrt{v_x^2 + v_y^2} \]

Plugging in the values:
\[ v = \sqrt{(25.0)^2 + (190)^2} \]
\[ v = \sqrt{625 + 36100} \]
\[ v = \sqrt{36725} \]
\[ v \approx 191.63 \text{ m/s} \]

Thus, the magnitude of the velocity of the plane is approximately 191.63 m/s.