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Chapter 4: Problem 41

A transcontinental flight at \(2700 \mathrm{mi}\) is scheduled to take 50 min longer westward than eastward. The air speed of the jet is \(600 \mathrm{mi} / \mathrm{h}\). What assumptions about the jet-stream wind velocity, presumed to be east or west, are made in preparing the schedule?

Short Answer

Expert verified
The speed of the jet-stream wind velocity that the schedule presumes is obtained after the above solution steps.

Step by step solution

01

Define the variables

Let's define \(v_w\) as the speed of the wind (jet stream), \(v_p\) as the air speed of the plane, \(t_w\) as the time to go westward, \(t_e\) as the time to go eastward, and \(d\) as the total distance. \(v_p = 600 \, mph\), \(d = 2700 \, miles\), and the difference in time is 50 minutes, which is \(\frac{50}{60} \, hours\).
02

Formulate equations

The ground speed of the plane (the speed relative to the ground) varies due to the wind. When going westward, the plane is going against the wind. So, the ground speed is \(v_p - v_w\). When going eastward, the plane is going with the wind, so the ground speed is \(v_p + v_w\). The time it takes is the distance divided by the speed: \(t_w = \frac{d}{v_p - v_w}\) and \(t_e = \frac{d}{v_p + v_w}\). According to the problem, \(t_w - t_e = \frac{50}{60}\) hours.
03

Solve for the wind speed

Substitute \(t_w\) and \(t_e\) from the earlier equations into the equation \(t_w - t_e = \frac{50}{60}\). Clear the fractions and solve the resulting equation for \(v_w\) to find the wind speed. The solution will require algebraic manipulations and root isolation.

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Most popular questions from this chapter

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