Chapter 8.3, Problem 46AYU

Revising a Flight Plan In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was ${10}^{\circ }$ in error, as indicated in the figure.

a. If the aircraft maintains an average speed of 220 miles per hour, and if the error in direction is discovered after 15 minutes, through what angle should the pilot turn to head toward Louisville?

b. What new average speed should the pilot maintain so that the total time of the trip is 90 minutes?

To determine

To find:

a. If the aircraft maintains an average speed of 220 miles per hour, and if the error in direction is discovered after 15 minutes, through what angle should the pilot turn to head toward Louisville?

b. What new average speed should the pilot maintain so that the total time of the trip is 90 minutes?

Answer to Problem 46AYU

Solution:

a. The pilot should turn at an angle of $12°$

b. New average speed should the pilot maintain so that the total time of the trip is 90 minutes is 220 miles/hr.

Explanation of Solution

Given:

In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was $10°$ in error, as indicated in the figure.

Formula used:

$c^2 = a^2 + b^2 - 2ab\text{cos}C$

Calculation:

a. The distance the plane would have flown after $15 \text{mins} = 220(0.25) = 55 \text{miles}$.

$a = 55, b = 330 \text{and} C = 10°$

$c^2 = a^2 + b^2 - 2ab\text{cos}C$

$c^2 = {55}^2 + {330}^2 - 2 * 55 * 330\text{cos}10°$

$c \approx 275$

Find the measure of the angle opposite to the 330 mile side.

$\text{cos}B = \frac{a^2 + c^2 - b^2}{2ac}$

$\text{Cos}B = \frac{\left(55² + 275² - 330²\right)}{2 * 55 * 330}$

$B \approx 168°$

The pilot should turn at an angle of $180° - 168° = 12°$

b. The total trip must take 90 minutes

$\text{Time} \text{taken} \text{already} = 15 \text{minutes}$.

$\text{Remaining} \text{time} = 75 \text{minutes} = 1.25 \text{hours}$.

$Speed = \frac{dis\text{tan}ce}{time}$

$speed = \frac{275}{1.25} = 220miles/hr$

new average speed should the pilot maintain so that the total time of the trip is 90 minutes is 220 miles/hr.