two sailboats leave a harbor in the bahamas

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word problem with boats and directions

• Thread starter 88m
• Start date Jan 24, 2008
• Jan 24, 2008

Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 20 mph in a direction 330°. The second sails at 34 mph in a direction 220°. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats? 89.9 miles 70.5 miles 58.5 miles 95.9 miles my instructor is being a hard @$$ and is not helping me here. i don't know the right formula and how to insert the values into it. SO please someone get me started.  

Super Moderator

Use the law of cosines. The angle is 110 degrees and you can easily calculate the two side lengths by using d=rt.  

88m said: my instructor is being a hard @$$ and is not helping me here. Click to expand...

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Solve the problem. Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 23 mph in a direction 350°. The second sails at 32 mph in a direction 190°. Assuming that both boats maintain speed and heading, after 4 hours, how far apart are the boats? 134.4 miles 168.4 miles 153.9 miles 216.7 miles Nex

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SOLUTION: Two ships leave harbor at the same time. The first sails North 15 degress West at 25 knots. The second sails North 32 degress East at 20 knots. After 2 hours, how far apart are the

Watch CBS News

Russian military exercises in the Caribbean: Here's what to expect

By Alex Sundby

Updated on: June 12, 2024 / 8:15 PM EDT / CBS News

Three Russian ships and a nuclear-powered submarine arrived in Cuban waters Wednesday ahead of military exercises  in the Caribbean. While the exercises aren't considered a threat to the U.S., American ships were deployed to shadow the Russians, U.S. officials told CBS News.

The Russian warships  were seen arriving in Havana's harbor on Wednesday morning and were expected to stay in Cuba until Monday. White House national security adviser Jake Sullivan told reporters on Air Force One on Wednesday the U.S. was closely monitoring the Russian ships.

"We have seen this kind of thing before and we expect to see this kind of thing again," Sullivan said.

The U.S. intelligence community has assessed that the submarine is nuclear powered but it isn't carrying nuclear weapons, CBS News national security correspondent David Martin reported. White House national security spokesman John Kirby told CBS News senior White House and political correspondent Ed O'Keefe last week that there was no indication nuclear weapons would be "at play" during the vessels' time in the Caribbean.

What Russian ships are in Cuba?

According to the Cuban Foreign Ministry, the three Russian ships are a frigate, a fleet oil tanker and a salvage tug. The three ships and the submarine headed across the Atlantic separately, Martin reported.

Russia has used the frigate, the Admiral Gorshkov, to test its Zircon hypersonic cruise missiles , according to the Reuters news agency.

Two American destroyers and two ships that tow sonar equipment behind them were shadowing the submarine, Martin reported. Another destroyer and a U.S. Coast Guard cutter were shadowing the three Russian ships. The U.S. Navy also used little sailboats fitted with cameras, known as sail drones, to shadow the Russian ships as they got close to Cuba.

The Admiral Gorshkov and the submarine carried out drills in the Atlantic that simulated a missile strike on enemy ships, the Russian Defense Ministry said Tuesday, according to the Associated Press.

While the Russian ships are in Cuba, the U.S. Navy ships shadowing them are expected to wait for the Russians and continue shadowing them when they leave port, Martin reported.

The ships' arrival in Havana — which the Cuban Foreign Ministry said was expected to include the fanfare of one Russian ship firing 21 salvos in a salute to Cuba — comes ahead of Russia carrying out air and naval exercises in the Caribbean in the coming weeks, Martin reported.

The exercises, which will include long-range bombers, will be the first simultaneous air and naval maneuvers Russia has carried out in the Caribbean since 2019, Martin reported. The exercises will be conducted over the summer, culminating in a worldwide naval exercise in the fall.

"Clearly this is them signaling their displeasure about what we're doing for Ukraine ," Kirby told O'Keefe. "So we're going to watch it, we're going to monitor it, it's not unexpected. … But we don't anticipate, we don't expect that there'll be any imminent threat or any threat at all, quite frankly, to American national security in the region, in the Caribbean region, or anywhere else."

The Russian ships are expected to head to Venezuela after Cuba, but it's unclear what the submarine will do, Martin reported.

What was the Cuban missile crisis?

The events in the Caribbean are different from the Cuban missile crisis that happened over 60 years ago. The 1962 crisis unfolded after the U.S. discovered launch sites in Cuba for Soviet ballistic nuclear missiles.

Over the course of 13 days, the crisis brought the Soviet Union and the U.S. dangerously close to nuclear war. A potential conflict was averted when the Kennedy administration reached a deal with the Kremlin for the missiles to be removed from Cuba.

Alex Sundby is a senior editor at CBSNews.com. In addition to editing content, Alex also covers breaking news, writing about crime and severe weather as well as everything from multistate lottery jackpots to the July Fourth hot dog eating contest.

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Boaters' safety concerns raised after Vancouver seaplane collision

2 people were hospitalized after saturday collision in coal harbour, which involved a harbour air plane.

Seaplane crashes into boat in Vancouver's Coal Harbour

Social sharing.

After multiple people were injured following a collision between a seaplane and a pleasure boat on Saturday, boaters are sharing tips on how to stay safe on Vancouver's waters.

Two people were hospitalized after a Harbour Air seaplane taking off from the nearby Harbour Flight Centre hit a boat  near Stanley Park on Saturday afternoon.

Canada's Transportation Safety Board (TSB) is investigating the collision. The plane's five passengers and pilot were not hurt, but people on the pleasure boat suffered injuries.

The crash has sparked calls for more safety measures in and around Burrard Inlet where the collision occurred, which sees thousands of recreational boaters every summer but also serves as the route for commercial vessels, tugboats and cruise ships. 

The Vancouver Fraser Port Authority is responsible for monitoring ship traffic in the inlet. Its harbour master, Sean Baxter, said anyone going out on the water should check the port's website ahead of time to see what areas they're allowed to access.

"It's important that recreational vessels look and watch out for larger vessels, as well as seaplanes," he said. "These types of port users have limited visibility, so don't assume that they can see you.

"We encourage everyone to listen, including listening for aircraft ... planes landing and taking off need plenty of space."

Who has the right of way?

While the TSB is investigating the exact cause of Saturday's crash, it has led to questions over which vessel has the right of way on the water.

• 2 hospitalized after seaplane goes down in Vancouver: officials

Ian Gilson, director of the Canadian Safe Boating Council, says it comes down to which vessel is more maneuverable.

"The vessel that is least maneuverable is the one that has the right of way," he told Michelle Eliot, host of CBC's  BC Today . "When a floatplane is either landing or taking off, it cannot change its course.

"So any other objects on the water have the responsibility to give way and to stay well clear."

Floatplane or boat: Which has the right of way in Burrard Inlet?

Statistics Canada says almost 6.5 million boating trips were taken between July and September 2021, with Gilson estimating that more than 16 million recreational boating trips are taken each year.

He says that people looking to hit the waters this summer should be mindful of boating safety tips , including wearing a life jacket, as ship traffic increases in and around Vancouver.

Calls for more buoys

Daniel and Candice Hecjman said they had close encounters with two different seaplanes while sailing in Coal Harbour in February 2019.

The couple is calling for more buoys and lights in Burrard Inlet to warn boaters to avoid areas where seaplanes can land.

"If the planes knew exactly where they're supposed to take off and land, then boaters will never go in that zone," Daniel said.

In response to a question about adding more buoys, a spokesperson for the port authority said that it regularly publishes procedures in its port information guide to ensure safety on the waterways.

"Since an active investigation of the incident is currently underway by the [TSB], we will await to receive the outcomes of their findings to determine if any of our procedures need to be updated," the spokesperson wrote.

No licence needed for rentals

Bruce Hayne, the executive director of Boating B.C., says that anyone new to boating should stick to less-populated areas to ensure safety.

"It's just like when you first get your [driving] licence, you probably don't want to hop onto the highway and get into heavy traffic," he said. "You want to start slowly and get comfortable with your vessel."

• Safe Boating Awareness Week aims to keep boaters safe all season

Hayne pointed out that in B.C., residents do not require a pleasure craft operator card if they are simply renting a pleasure boat—although he says there are discussions about changing that.

However, he says boat rental companies must provide safety checklists and demonstrations when renting boats, which should help new boaters operate safely.

ABOUT THE AUTHOR

Akshay Kulkarni is a journalist who has worked at CBC British Columbia since 2021. Based in Vancouver, he has covered breaking news, and written features about the pandemic and toxic drug crisis. He is most interested in data-driven stories. You can email him at [email protected].

• Follow Akshay Kulkarni on Twitter

With files from Jon Hernandez, Yvette Brend and BC Today

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