Chapter 4.8, Problem 38E

a.

To determine

How long will it take the yacht to make the trip?

Answer to Problem 38E

  $\boxed{21.4}$

Explanation of Solution

Given information:

A privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S $1.4°E.$ The yacht averages a speed of $20$ knots over the $428$ -nautical-mile trip.

How long will it take the yacht to make the trip?

Calculation:

Assume that a privately yacht leaves a dock in myrtle beach, south Carolina and heads towards Freeport in the Bahamas at a bearing of $S1.4°E$

Let the yacht averages a speed of $20$ knots over a trip of $428$ -nuatical miles

Since the distance travelled is $428$ nautical-miles and the speed is $20$ knot (the knot is defined as one nautical mile per hour).

So the time taken by the yacht to make the trip is

  $\frac{428}{20}=21.4$

Hence, the yacht will taken $\boxed{21.4}$ hours to make the trip.

b.

To determine

How far east and south is the yacht after $12$ hours?

Answer to Problem 38E

  $\boxed{239.93nautical-miles}$

Explanation of Solution

Given information:

A privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S $1.4°E.$ The yacht averages a speed of $20$ knots over the $428$ -nautical-mile trip.

How far east and south is the yacht after $12$ hours?

Calculation:

Since the yacht is travelling at a speed of $20$ knots

Therefore, the distance travelled by the yacht in $12$ hours is given by

  $20\times 12=240$ Nautical-miles

Since the bearing is $S1.4E$

Therefore, after $12$ hours, in the east, the yacht is

  $\begin{array}{l}240\times \sin \left(1.4°\right)=240\times 0.0244\\ =5.86\end{array}$

Thus, the yacht is $\boxed{5.86nautical-miles}$ east after $12$ hours

Also, after $12$ hours, in the east, the yacht is

  $\begin{array}{l}240\times \cos \left(1.4°\right)=240\times 0.999\\ 239.93\end{array}$

Thus, the yacht is $\boxed{239.93nautical-miles}$ south after $12$ hours

C

To determine

A plane leaves Myrtle Beach to fly to Freeport. At what bearing should it travel?

Answer to Problem 38E

  $\boxed{178.6°}$

Explanation of Solution

Given information:

A privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S $1.4°E.$ The yacht averages a speed of $20$ knots over the $428$ -nautical-mile trip.

A plane leaves Myrtle Beach to fly to Freeport. At what bearing should it travel?

Calculation:

The bearing that should be taken by the plane in its travel from Myrtle Beach to Freeport is

  $\begin{array}{l}180°-1.4°=\boxed{178.6°}\\ \end{array}$