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 direction of the velocity of the bird? θ = ?°

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 velocity in x - direction) \(v_x=3.95\space m/s\).

Step2: Use tangent function for angle

The direction of the velocity vector (angle \(\theta\) with respect to x - axis) is given by \(\tan\theta=\frac{v_y}{v_x}\).

Substitute \(v_y = 25.5\) and \(v_x = 3.95\) into the formula:
\(\tan\theta=\frac{25.5}{3.95}\approx6.4557\)

Step3: Find the angle

To find \(\theta\), we take the arctangent (inverse tangent) of \(6.4557\):
\(\theta=\arctan(6.4557)\)

Using a calculator, \(\theta\approx81.1^{\circ}\) (measured from the x - axis towards the y - axis)

Answer:

\(81.1\) (The answer may vary slightly depending on the calculator's precision, but the approximate value is around \(81.1^{\circ}\))