Question

7. With a tailwind, a bird flew at a ground speed of 3 mi/h. Flying the same path against the same wind, the bird travels at a ground speed of 1.5 mi/h. What is the bird's air speed? What is the wind speed?

Answer 1

Speed of bird with respect to the wind = Bird's air speed = 2.25 mi/h

Speed of the wind with respect to the ground = Wind's speed = 0.75 mi/h

Step-by-step explanation

Relative speed is usually given in terms of speed of a body A with respect to another body B (Vab)

Vab = Va - Vb

Vab = Speed of A relative to B

Va = Speed of A

Vb = Speed of B

So, for this question, when the bird is travelling in the same direction of wind, the speed of the bird with respect to the ground is 3 mi/h

(Speed of bird with respect to the wind)

= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)

Speed of bird with respect to the wind = x

Speed of bird with respect to ground = 3 mi/h

Speed of the wind with respect to the ground = y

(Speed of bird with respect to the wind)

= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)

x = 3 - y

When the bird is travelling in the opposite direction, the speed of the bird with respect to the ground is 1.5 mi/h

Speed of bird with respect to the wind = x

Speed of bird with respect to ground = 1.5 mi/h

Speed of the wind with respect to the ground = -y (Negative since the wind is in the opposite direction)

(Speed of bird with respect to the wind)

= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)

x = 1.5 - (-y)

x = 1.5 + y

We can the solve this system of equations

x = 3 - y

x = 1.5 + y

1.5 + y = 3 - y

y + y = 3 - 1.5

2y = 1.5

Divide both sides by 2

(2y/2) = (1.5/2)

y = 0.75 mi/h

x = 1.5 + y

x = 1.5 + 0.75

x = 2.25 mi/h

Hope this Helps!!!