Chapter 6.3, Problem 110E

(a)

To determine

To draw: The figure of given vectors and speed.

Answer to Problem 110E

  

Explanation of Solution

Given: A commercial jet is flying from Miami to Seatle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing is ${332}^{\circ }$ . The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

Let the Jet’s velocity with respect to air be $580$ miles per hour and bearing is ${332}^{\circ }$

So, vector representation, $V_{JW}=580\cos {332}^{\circ }i+580\sin {332}^{\circ }j$

The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

The vector representation of wind, $V_W=60\cos {225}^{\circ }i+60\sin {225}^{\circ }j$

  

(b)

To determine

To write: The velocity of the wind as a vector in component form.

Answer to Problem 110E

  $V_W=-42.43i-42.43j$

Explanation of Solution

Given: A commercial jet is flying from Miami to Seatle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing is ${332}^{\circ }$ . The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

Let the Jet’s velocity with respect to air be $580$ miles per hour and bearing is ${332}^{\circ }$

So, vector representation, $V_{JW}=580\cos {332}^{\circ }i+580\sin {332}^{\circ }j$

The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

The vector representation of wind in component form, $V_W=60\cos {225}^{\circ }i+60\sin {225}^{\circ }j$

  $V_W=-42.43i-42.43j$

(c)

To determine

To write: The velocity of the jet relative to the air as a vector in component form.

Answer to Problem 110E

  $V_{JW}=512.11i-272.29j$

Explanation of Solution

Given: A commercial jet is flying from Miami to Seatle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing is ${332}^{\circ }$ . The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

Let the Jet’s velocity with respect to air be $580$ miles per hour and bearing is ${332}^{\circ }$

So, vector representation, $V_{JW}=580\cos {332}^{\circ }i+580\sin {332}^{\circ }j$

  $V_{JW}=512.11i-272.29j$

(d)

To determine

To find: The speed of the jet relative to the ground.

Answer to Problem 110E

554.74 miles per hour.

Explanation of Solution

Given: A commercial jet is flying from Miami to Seatle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing is ${332}^{\circ }$ . The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

Let the Jet’s velocity with respect to air be $580$ miles per hour and bearing is ${332}^{\circ }$

So, vector representation, $V_{JW}=580\cos {332}^{\circ }i+580\sin {332}^{\circ }j$

  $V_{JW}=512.11i-272.29j$

The vector representation of wind in component form, $V_W=60\cos {225}^{\circ }i+60\sin {225}^{\circ }j$

  $V_W=-42.43i-42.43j$

Velocity of jet with respect to ground, $V_J=V_{JW}+V_W$

  $\begin{array}{l}{V}_J=\left(512.11i-272.29j\right)+\left(-42.43i-42.43j\right)\\ V_J=398.97i-385.43j\end{array}$

Speed of jet, $\left|V_J\right|=\sqrt{{398.97}^2+{\left(-385.43\right)}^2}=554.74$

The speed of jet 554.74 miles per hour.

(e)

To determine

To find: The true direction of the jet.

Answer to Problem 110E

  $\theta \approx {316}^{\circ }$

Explanation of Solution

Given: A commercial jet is flying from Miami to Seatle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing is ${332}^{\circ }$ . The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour.

Let the Jet’s velocity with respect to air be $580$ miles per hour and bearing is ${332}^{\circ }$

So, vector representation, $V_{JW}=580\cos {332}^{\circ }i+580\sin {332}^{\circ }j$

  $V_{JW}=512.11i-272.29j$

The vector representation of wind in component form, $V_W=60\cos {225}^{\circ }i+60\sin {225}^{\circ }j$

  $V_W=-42.43i-42.43j$

Velocity of jet with respect to ground, $V_J=V_{JW}+V_W$

  $\begin{array}{l}{V}_J=\left(512.11i-272.29j\right)+\left(-42.43i-42.43j\right)\\ V_J=398.97i-385.43j\end{array}$

Direction of the Jet, $\theta ={\tan }^{-1}\left(-\frac{385.43}{398.97}\right)$

  $\theta \approx {316}^{\circ }$