Question

a bird is flying at 25.5 m/s in the y-direction. the wind is blowing at 3.95 m/s in the x-direction. what is the magnitude of the velocity of the bird? v = ? m/s

Explanation:

Step1: Identify velocity components

The bird's velocity in y - direction, \(v_y = 25.5\space m/s\), and wind (which affects the bird's x - velocity) \(v_x=3.95\space m/s\).

Step2: Use Pythagorean theorem for magnitude

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 \(v_x = 3.95\space m/s\) and \(v_y=25.5\space m/s\) into the formula:

\(v_x^{2}=(3.95)^{2}=15.6025\)

\(v_y^{2}=(25.5)^{2}=650.25\)

\(v_x^{2}+v_y^{2}=15.6025 + 650.25=665.8525\)

Then \(v=\sqrt{665.8525}\approx25.8\space m/s\) (rounded to three significant figures)

Answer:

\(25.8\)