You are spending the summer as an assistant learning how to navigate on a large ship carrying freight across Lake Erie. One day, you and your ship are to travel across the lake a distance of 200 km traveling due north from your origin port to your destination port. Just as you leave your origin port, the navigation electronics go down. The captain continues sailing, claiming he can depend on his years of experience on the water as a guide. The engineers work on the navigation system while the ship continues to sail, and winds and waves push it off course. Eventually, enough of the navigation system comes back up to tell you your location. The system tells you that your current position is 50.0 km north of the origin port and 25.0 km east of the port. The captain is a little embarrassed that his ship is so far off course and barks an order to you to tell him immediately what heading he should set from your current position to the destination port. Give him an appropriate heading angle.
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Chapter 3 Solutions
Physics for Scientists and Engineers
- In your new job, you are the technical advisor for the writers of a gangster movie about Bonnie and Clyde. In one scene Bonnie and Clyde try to flee from one state to another. If they get across the state line, they could evade capture, at least for a while until they become Federal fugitives. In the script, Bonnie is driving down the highway at 108 km/hr and passes a concealed police car that is 1 km from the state line. The instant Bonnie and Clyde pass the patrol car, the cop pulls onto the highway and accelerates at a constant rate of 2 m/s2. The writers want to know if they make it across the state line before the pursuing cop catches up with themarrow_forwardA sailboat sails from Marblehead Harbor directly east for 45 nautical miles, then 60 degree south of east for 20 nautical miles, returns to an easterly heading for 30 nautical miles, and sails 30 degreeeast of north for 10 nautical miles, then west for 62 nautical miles. At that time the boat becomes becalmed and the auxiliary engine fails to start. The crew decides to notify the Coast Guard of their position. What is their position?arrow_forwardOliver Queen is stranded on the remote island of Lian Yu. He knows that here is an enemy camp 15 miles away directly northeast of his current position. He hikes for 6 miles along a path that runs 28 degrees north of due east then changes courses and hikes another 7 miles in the direction 41 degrees east of due north. How far is he from the camp? In what direction should he hike to reach it?arrow_forward
- As it passes Grand Bahamas Islands, the eye of the hurricane Katrina is moving in a direction of 60 0 north of west at a speed of 50 kph. Three hours later, it shifts due north where its speed slows to 25 kph. How far from the Grand Bahamas is the eye of the hurricane 4.5 hrs. after it passes over the island?arrow_forwardOur garage mechanic is flying from St. Hubert to Québec City in a Cessna. His Cessna flies at an air-speed of 170.0 km/hr. To make it easy he decides to fly along Route 30 from St. Hubert, which is straight North out of St Hubert. (In the old days the CPR railway across Western Canada was referred to by bush-pilots as the "Iron Compass". As a non-counting trivia question, why?). However, to follow along highway 30 he finds that he must point his plane in the direction 4.5 degrees West of North. By following the highway markers he finds that he is actually travelling North at 190.0 km/hr. Being a clever person (he recently got an "A" in physics 101 but decided to go into garage mechanics instead of medicine) he quickly calculates the wind-speed to be (answer below in kilometers per hour). a) What is the wind speed he calculated? b) What is the direction of the wind? Give the direction in degrees relative to North; positive for East, negative for Westarrow_forwardA ship travels on a N 50° E course. The ship travels until it is due north of a port which is 10 nautical miles due east of the port from which the ship originated. How far did the ship travel?arrow_forward
- Your garage mechanic is flying from St. Hubert to Québec City in a Cessna. His Cessna flies at an air-speed of 150.0 km/hr. To make it easy he decides to fly along Route 30 from St. Hubert, which is straight North out of St Hubert. (In the old days the CPR railway across Western Canada was referred to by bush-pilots as the "Iron Compass". As a non-counting trivia question, why?). However, to follow along highway 30 he finds that he must point his plane in the direction 3 degrees West of North. By following the highway markers he finds that he is actually travelling North at 149.0 km/hr. Being a clever person (he recently got an "A" in physics 101 but decided to go into garage mechanics instead of medicine) he quickly calculates the wind-speed to be (answer below in kilometers per hour). What is the direction of the wind? Give the direction in degrees relative to North; positive for East, negative for Westarrow_forwardSubmarine A leaves a port and stations itself at a distance 37 km to the northeast. Submarine B leaves from the same port and stations itself 37 km to the west. What is the distance between the two submarines. The answer should be in km and in two decimal places.arrow_forwardA radar station sends a signal to a ship which is located a distance 13.8 kilometers from the station at bearing 136° clockwise from the north. At the same moment, a helicopter is at a horizontal range of 19.6 kilometers, at bearing 146° clockwise from the north, with an elevation of 2.56 kilometers. Let east be the î direction, north be the ĵ direction, and up be the direction. a) What If? The ship begins to sink at a rate of 5.50 m/s. Write the position vector (in km) of the ship relative to the helicopter as a function of time as the ship sinks. Assume that the helicopter remains hovering at its initial position and that the sinking rate remains the same even after the ship sinks under the surface.arrow_forward
- Problem 5: An athlete crosses a 28 m wide river by swimming perpendicular to the water current at a speed of 0.85 m/s relative to the water. He reaches the opposite side at a distance 39 m downstream from his starting point. Randomized Variables w = 28 m d = 39 m Vs = 0.85 m/sarrow_forwardA group of Boy Scouts on a straight trail headed N30.6 E found the trail led through a briar patch. They chose to walk 156 meters due east along the south edge of the briar patch, then due north along the east edge of the patch back to the trail. How much farther did they walk to avoid walking through the briar patch?arrow_forwardOne day, Sofia goes hiking at a nearby nature preserve. At first, she follows the straight, clearly marked trails. From the trailhead, she travels 2.00 miles2.00 miles down the first trail. Then, she turns 30.0 degrees to the left to follow a second trail for 1.10 miles. Next, she turns 160.0 degrees to her right to follow a third trail for 1.90 miles. At this point, Sofia is getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead her deeper into the woods. She would like to take a shortcut directly through the woods (ignoring the trails). What distance ?SC does she have to walk to take a shortcut directly back to her starting point? ?SC= Through what angle ?SC should she turn to the right in order to take the shortcut directly back to her starting point? ?SC=arrow_forward
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