Question

a plane is flying at 115 m/s in the y - direction. the wind is blowing at 75.0 m/s in the x - direction. what is the magnitude of the velocity of the plane? v = ? m/s

Explanation:

Step1: Identify the components

The plane's velocity in y - direction \(v_y = 115\space m/s\), wind (which contributes to x - direction velocity of plane) \(v_x=75.0\space m/s\)

Step2: Use Pythagorean theorem for magnitude of velocity

The magnitude of the resultant velocity \(v\) of a vector with components \(v_x\) and \(v_y\) is given by \(v=\sqrt{v_x^{2}+v_y^{2}}\)
Substitute \(v_x = 75.0\space m/s\) and \(v_y=115\space m/s\) into the formula:
\(v=\sqrt{(75.0)^{2}+(115)^{2}}\)
First, calculate \((75.0)^{2}=75.0\times75.0 = 5625\) and \((115)^{2}=115\times115 = 13225\)
Then, \(v=\sqrt{5625 + 13225}=\sqrt{18850}\approx137.3\space m/s\)

Answer:

\(137.3\) (or more precisely, \(\sqrt{18850}\approx137.3\))