In the LORAN (LOng RAnge Navigation) Radio Navigation System, Two $A$

question 21

Multiple Choice

In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at $A$ and $B$ transmit simultaneous signals to a ship or an aircraft located at $P$ . The onboard computer converts the time difference in receiving these signals into a distance difference $| A | - | B |$ , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure) . Suppose that station $B$ is located $\mathrm { L } = 480 \mathrm { mi }$ due east of station $A$ on a coastline. A ship received the signal from $B 1280$ microseconds $( \mu s )$ before it received the signal from $A$ .
Assuming that radio signals travel at a speed of $1000 \mathrm { ft } / \mu \mathrm { s }$ and if the ship is due north of $B$ , how far off the coastline is the ship? Round your answer to the nearest mile.

• A) 355 miles
• B) 358 miles
• C) 357 miles
• D) 354 miles
• E) 356 miles

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Definitions:

Pigs

Domesticated animals farmed for their meat (pork), as well as their skin, bristles, and other parts.

Cattle

domesticated bovine animals kept for milk, meat, or as draught animals.

Sugar Production

The process of growing sugar crops, particularly sugarcane and sugar beet, and extracting sugar for consumption and commercial use.

South American Country

Any sovereign state located on the continent of South America.