Question

A seagull flies at a velocity of 9.0 m/s straight into the wind.

(a) If it takes the bird 20 min to travel 6.0 km relative to the Earth, what is the velocity of the wind?

(b) If the bird turns around and flies with the wind, how long will he take to return 6.0 km?

(c) Discuss how the wind affects the total round-trip time compared to what it would be with no wind.

Short answer

(a) The velocity of the wind relative to earth is-4m/s.

(b) The time taken when the bird is moving with the wind will be 7.7 min.

(C) Due to wind, bird takes (20 – 7.7) min less time compared with no wind.

Step-by-step solution

Definition of velocity

The directional speed of an item in motion is an indication of its rate of change in position as seen from a specific point of view and measured by a specific time standard.

Given data

The velocity can be said as V_i is9.0m/s The velocity is making some angle with the x axis.

The bird travels in x direction is6km that is distance in meter =6000meter

The time taken by bird is20min, which can be converted into seconds

t = 20 x 60 = 1200 s

The velocity of the bird relative to the wind is V_bw 9m/s

The gravitational acceleration is-9.8m/s²

Velocity of the bird opposite to wind

The velocity of the bird

$$\begin{gathered} \stackrel{-}{V_b}=\frac{x}{t} \\ \stackrel{-}{V_b}=\frac{6000}{1200} \\ \stackrel{-}{V_b}=5m/s \end{gathered}$$

The velocity of the bird relative to earth is 5 m/s.

a. The velocity of the wind will be

$$\begin{gathered} V_{we}=V_{wb}+V_{be} \\ {V}_{we}=\left(-9\right)+5 \\ {V}_{we}=-4m/s \end{gathered}$$

The velocity of the wind relative to earth is -4 m/s.

Time of the bird to return 6 km with the direction of wind

b. Time of the bird to return 6 km with the direction of wind is

$\overline{V_{be}}=\frac{x_e}{t}$

The velocity of the bird relative to the earth

$$\begin{gathered} {\text{V}}_{be}{\text{=V}}_{bw}{\text{+V}}_{we} \\ {\text{V}}_{be}=\left(-9\right)+\left(-4\right) \\ {\text{V}}_{be}=-13m/s \end{gathered}$$

Putting the value of velocity in the equation

$$\begin{gathered} \stackrel{-}{V_{be}}=\frac{X_e}{t} \\ -13=\frac{-6000}{t} \\ t=\frac{6000}{13} \\ t=462s=7.7min \end{gathered}$$

The time taken when the bird is moving with the wind will be 7.7 min .

(C) Due to wind, bird takes (20 – 7.7) min less time compared with no wind.