A seagull flies with an air speed of 14m/s straight into the wind. Include units as appropriate below. If under these conditions it takes the bird 20min to travel 6km, what is the speed of the wind?

Question

A seagull flies with an air speed of 14m/s14m/s straight into the wind. Include units as appropriate below.

(a) If under these conditions it takes the bird 20min20min to travel 6km6km, what is the speed of the wind?

(b) If the bird turns around and flies with the wind, how long will the bird take to return 6km6km?

Answer 1

(a) If under these conditions it takes the bird 20min to travel 6km, what is the speed of the wind?

Let:

v_g : the ground speed of the gull, > 0

v_a : the air speed of the gull; 14 m/s

w : the velocity of the wind, < 0 (opposite of the direction the gull is flying)

The air speed of the gull is the sum of it's ground speed, and the speed of the wind. (If the wind is in the same direction the gull is flying, their signs will be the same so you just add them together):

v_a = v_g + w

It takes the bird 20 min to fly 6 km at a speed equal to its ground speed, so plugging those values into:

x = v_g × t

... gives:

v_g = x/t = 6 km /(20 min) = 6000 m/(1200 s) = 5 m/s

Then the speed of the wind is:

w = v_a - v_g = 14 m/s - 5 m/s = 9 m/s

(b) If the bird turns around and flies with the wind, how long will the bird take to return 6km?

We can solve this by changing the sign of the wind speed, and recalculating the ground speed:

v_g = v_a - w = 14 m/s - (-9 m/s ) = 23 m/s

The time taken will now be:

t = x/v_g = 6000 m/(23 m/s) = 260.9 s