Question

Lucas programs his quadcopter to fly with a velocity (speed and direction) vector \vec{p} = 4\hat i + 7\hat j p ​ =4 i ^ +7 j ^ ​ p, with, vector, on top, equals, 4, i, with, hat, on top, plus, 7, j, with, hat, on top, which should send it straight at its target (in the absence of wind). To his dismay, his quadcopter actually moves with a velocity vector \vec{a} = 2\hat i + 8\hat j a =2 i ^ +8 j ^ ​ a, with, vector, on top, equals, 2, i, with, hat, on top, plus, 8, j, with, hat, on top. (Speeds are given in meters per second, \text{m}/\text{s}m/sstart text, m, end text, slash, start text, s, end text.) What is the speed of the wind?

Answer 1

Speed: 2.2

Wind: 153

Answer 2

Velocity of the wind relative to the ground = (2î - ĵ) m/s

Speed of the wind = √5 m/s = 2.236 m/s

Explanation:

Relative velocity of a body A with respect to B is given as the velocity of body A with respect to a reference frame C minus the velocity of body B with respect to a reference frame C.

That is

Vab = Vac - Vbc

Let the quadcopter be body A

The wind be body B

And the earth be the reference frame C.

Vac = velocity of the quadcopter relative to the ground = (4î + 7ĵ) m/s

Vab = velocity of the quadcopter with respect to the wind = (2î + 8ĵ) m/s

Vbc = velocity of the wind relative to the ground = ?

Vab = Vac - Vbc

(2î + 8ĵ) = (4î + 7ĵ) - Vbc

Vbc = (4î + 7ĵ) - (2î + 8ĵ)

Vbc = (2î - ĵ) m/s

The speed of the wind is the magnitude of its velocity

Magnitude of Vbc = √[2² + (-1)²] = √5 = 2.236 m/s

Hope this Helps!!!