Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.05 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 28.6° north of east at a speed of 1.57 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.16 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?

A 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?

A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?

A jetliner can fly 4.8 hours on a full load of fuel. Without any wind, it flies at a speed of 2.68 x102m/s. The plane is to make a round trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 69.9 m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home?

Jonah is walking along a trail. The trail heads east for 1350 meters, before turning north and continuing for 990 meters. At the end of the trail, what is Jonah's displacement vector? Options:  1670 m, 36.3∘36.3∘ north of east 1670 m, 36.3∘ east of north 2340 m, 31.0∘ east of north 2340 m, 31.0∘ north of east

3.37 The nose of an ultralight plane is pointed south, and its airspeed indicator shows 36 m/sm/s . The plane is in a 16 m/sm/s wind blowing toward the southwest relative to the earth.1. Letting x be east and y be north, find the components of v⃗ P/Ev→P/E (the velocity of the plane relative to the earth)2. Find the magnitude of v⃗ P/Ev→P/E. 3. Find the direction of v⃗ P/Ev→P/E.

A golfer on level ground attempts to drive a golf ball across a 50 meter wide pond by hitting the ball so that it travels initially at 25m/s at an angle of 45 degrees to the horizontal plane. How far will the golf ball travel?

One 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=

As an airplane taxies on the runway with a speed of 16.5 m>s,a flight attendant walks toward the tail of the plane with a speed of 1.22 m>s. What is the flight attendant’s speed relative to theground?

A submarine dives from the water surface at an angle of 30° below the horizontal, following a straight path 50 m long. How far is the submarine then below the water surface? (a) 50 m (b) (50 m)/sin 30° (c) (50 m) sin 30° (d) (50 m) cos 30° (e) none of those answers.