Question

A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is blowing due north with a speed of 30 mi/h. (Assume that the i vector points east, and the j vector points north.)
a. Express the velocity of the wind as a vector in component form.
b. Express the velocity of the jet relative to the air as a vector in component form.
c. Find the true velocity of the jet as a vector.
d. Find the true speed of the jet. (Round your answer to the nearest integer.)
e. Find the direction of the jet.

Answer 1

Answer:

a) V = 30j

b) U = 475i

c) W = 475i + 30j

d) true speed = 475.95mi/h

e) Direction = 3.62°

Explanation:

The speed of the jet is 475mi/h relative to air.

The wind speed is 30mi/h to the north.

a) The velocity of the wind represented by a ve tor v in component form is given by:

V = 30j

b) The velocity of the jet relative to the air represented by a vector U in component form is given by:

U = 475i

c) The true velocity of the jet as a vector W is represented as W is given by:

W = U + V = 475i + 30j

d) The true speed of the jet is given by:

W = Sqrt(475^2 +30^2)

W = Sqrt(225625 + 900)

W = Sqrt(226525)

W = 475.95mi/h

e) The direction of the jet is given by :

Theta = Tan^-1 (30/475)

Theta = Tan^-1(0.06316)

Theta = 3.62°